Some new trends in Lyapunov's direct method

Chapters in this book

1. I-IV I
2. Preface V
3. Table of Contents IX
4. List of Participants XL
5. Investigation of Oldrojt's viscoelastic model when viscous coefficient tends to zero 1
6. Nonlinear PDE problems in electrophotography 13
7. A special class of maximum principles with applications to nonlinear boundary value problems 25
8. Nonlinear mathematics in nonacademic settings 41
9. Motion of a graph by nonsmooth weighted curvature 47
10. Some results on heat flow in electric conductors 57
11. Global classical solutions to fully nonlinear wave equations 67
12. Solitons and domains in dipole chains 73
13. Nonlinear instabilities of steady and oscillatory wave convection in a rotating system 79
14. Bifurcations and chaos in predator-prey models with delay 87
15. On a new variant degree theory of mapping and its application 111
16. Solvability of semilinear operator equations and periodic solutions of differential equations 125
17. Solutions of semilinear equations in cones and wedges 137
18. On a nonlinear elliptic problem with subcritical and critical Sobolev exponent 149
19. Existence and bifurcation results for some semilinear elliptic equations on ℝN 161
20. Some remarks about the existence of positive solutions for elliptic systems 167
21. Sub- and supersolutions of nonlinear elliptic and parabolic problems 175
22. Positive solutions and boundary value problems of singular and nonsingular type 185
23. On the asymptotic behavior of laminar flow through a porous pipe 201
24. The monotone method for third order boundary value problems 211
25. Duality and variational principles for nonlinear hyperbolic equations 223
26. Decay and global existence for some nonlinear dissipative wave equations 233
27. On the philosophy of the spectral variable 241
28. Wave propagation in uniaxial nonconducting nonlinear thermoelastic solids 253
29. Approximation of dissipative hereditary systems 269
30. Stefan problems in several space variables with dynamic boundary conditions 281
31. Existence and multiplicity of periodic solutions for semilinear parabolic equations 291
32. Boundary integral solution of a nonlinear heat conduction problem 299
33. On the existence of travelling waves in reaction–diffusion systems 311
34. The strong maximum principle for cooperative periodic-parabolic systems and the existence of principal eigenvalues 323
35. Blowing-up of solutions of semilinear parabolic equations 335
36. An existence and uniqueness theorem for solutions of nonlocal parabolic partial differential equations 341
37. Open problems in nonlinear ordinary boundary value problems arising from the study of large-amplitude periodic oscillations in suspension bridges 349
38. One species extinction in an autonomous competition model 359
39. Periodic stability and reachability of nonlinear parabolic equations under boundary periodic perturbations 369
40. A criterion for asymptotic stability based on topological degree 383
41. Periodic solutions and subharmonic solutions for a class of planar systems of Lotka - Volterra type 395
42. Periodic boundary value problems for impulsive integro-ordinary differential equations 407
43. Some multiplicity results for subharmonic solutions to second order nonautonomous systems 417
44. New results in quenching 427
45. On the life span of solutions to nonlinear wave equations 435
46. Conversion and penetration fronts in combustion 445
47. The transition from decay to blow–up in some reaction–diffusion–convection equations 455
48. Numerical Experiments on the Ginzburg-Landau Equations 465
49. Counterexamples to the existence of inertial manifolds 477
50. Inverse problems versus an algebraic spectral method for nonlinear evolution equations 487
51. A finite difference scheme for an inverse heat equation 497
52. Nonlinear ill-posed problems 505
53. Maximum entropy regularization of nonlinear ill-posed problems 513
54. Variational derivatives in function spaces 527
55. Radial and nonradial solutions of a nonlinear scalar field equation 537
56. A geometric method for the periodic problem 549
57. Large perturbations of Toda lattices 561
58. Distribution of mass principle and its applications to nonlinear elliptic equations 571
59. Attractors of bipolar and non-Newtonian viscous fluids 583
60. Nonlinear dynamics in the low Reynolds number cylinder wake 597
61. The present status of the theory of the flow of a compressible viscous fluid through a pipe or parallel-wall channel 611
62. Laminar and turbulent film flows 623
63. Sensitivity equations for the k – ε turbulence model for ill-posed inverse problems in computational fluid dynamics 631
64. Large-time behavior of reaction-diffusion systems modeling combustion with complex chemistry 651
65. Stability analysis of the travelling wave solutions in burning solid propellants 661
66. Stability of travelling waves in combustion problems: a fully nonlinear approach 667
67. On the numerical analysis of buckling of general thin shells 681
68. Random fields in nonlinear structural problems 691
69. Geometrically nonlinear analysis of inelastic damaged shells 701
70. Moderate rotations of shells under circulatory loading 711
71. Further results on postbuckling behavior of shear deformable plates and shallow shells accounting for initial geometric imperfections 723
72. Failure prediction in composite laminates according to the layerwise plate theory 739
73. A theory for nonlinear static and transient analysis of composite laminates 753
74. Numerical methods for ODEs with hysteresis 765
75. P.D.E.s with hysteresis operators 775
76. Some limit results for relays 787
77. The Mróz model: A hysteresis operator for rate-independent plasticity 797
78. A differential model of fatigue in elastoplastic materials 807
79. Orientable and nonorientable minimal surfaces 819
80. Continuation methods in nonlinear elasticity 827
81. Bifurcation for variational inequalities and applications to elasticity 839
82. Infinite dimensional integrals in classical, stochastic and quantum nonlinear problems 849
83. Asymptotic formulas in capillarity 861
84. An envelope theorem for weak solutions of quasilinear elliptic boundary value problems 869
85. Group theoretical methods for finite-difference modeling 879
86. Two parameter problems for the p-Laplacian 891
87. Positive solutions of semilinear Neumann problems and Sobolev type inequalities 901
88. A free boundary eigenvalue problem 911
89. Measure valued solution of non-Newtonian compressible heat conductive fluid 925
90. Asymptotics for a class of weakly nonlinear wave equations with applications to some problems 945
91. Path optimization in flat and wrinkled labyrinths using arrays of active nonlinear circuits: traveling wave and its failure 953
92. An Oregonator based model for the influence of a radial electric field on the dynamics of spiral waves 965
93. Theorem about a weak impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities 977
94. Products of distributions in mathematical physics 989
95. A qualitative analysis of the potential and current driven semiconductor equations 1001
96. Author Index 1011
97. Differential-geometric computational methods for nonlinear problems 1017
98. Set-valued analysis, viability theory and partial differential inclusions 1039
99. Global stability, injectivity, and the Jacobian conjecture 1059
100. Theory of multipolar fluids 1073
101. Theory vs. relativity 1083
102. Difference equations and inequalities: a survey 1091
103. Invariant fiber bundles for nonautonomous difference systems 1109
104. Sign properties of Green's functions for difference equations 1121
105. Global Stability of Difference Equations 1131
106. Singular boundary value problems for higher order difference equations 1139
107. Asymptotic behavior and oscillation of general nonlinear difference equations 1151
108. Permanence and global attractivity in nonlinear difference equations 1161
109. Comparison theorems for a difference equation with memory 1173
110. Dichotomies for differential systems with impulsive effect 1181
111. Soliton-like solutions of the discrete wave equation 1193
112. Examples of Lyapunov functionals for non-differentiated equations 1203
113. A Lyapunov-Razumikhin method for functional differential equations 1215
114. Attractivity in nonautonomous equations by Liapunov's method 1223
115. New directions in the method of vector Lyapunov functions via cone valued Lyapunov functions 1233
116. A conjecture in Lyapunov method for functional differential equations 1239
117. Stability criteria for impulsive integro-differential equations 1247
118. Current state of the method of vector Lyapunov functions 1255
119. New approach to the dynamic programming for optimal control problems with state constraints 1269
120. Methods of stability theory for singularly perturbed problems with applications to dynamics 1279
121. On stability of steady motions of rigid body with liquid-filled cavity 1287
122. Some new trends in Lyapunov's direct method 1295
123. Uniform asymptotic stability in functional differential equations with finite delay 1303
124. Stability analysis of an HIV transmission model 1313
125. Stability of general ecological systems and neural networks systems 1325
126. On the asymptotic stability in differential systems by Lyapunov direct method 1341
127. Stability and attraction in impulsive semidynamical systems 1349
128. A universal integral invariant of non-autonomous dynamical systems 1357
129. Convergence in neutral equations with infinite delay arising from active compartmental systems 1361
130. An invariance principle of Lyapunov-Razumikhin type and compartmental systems 1371
131. On the existence of almost periodic solutions of nonlinear compartmental systems with time delays 1381
132. On numerical solutions for a class of nonlinear delay equations with time- and state-dependent delays 1391
133. Asymptotic periodicity in impulsive differential equations of retarded type with applications to compartmental models 1403
134. Variation of parameters formula and Lipschitz stability of nonlinear matrix differential equations 1415
135. Stability of a class of nonlinear continuous neural networks 1427
136. Roughness properties of (h, k)-dichotomies 1437
137. On the existence and qualitative properties of solutions for a nonlinear Neumann problem with critical exponent 1445
138. Behavior of nonoscillatory solutions of forced second order neutral delay equations 1457
139. Regularity and asymptotics of a similarity solution of an equation arising in boundary layer theory 1469
140. On solutions of a neutral equation with an oscillatory coefficient 1475
141. Asymptotic behavior of nonlinear neutral differential equations 1483
142. On oscillation of nonlinear first order differential equations with its application 1497
143. Topological and variational approaches for nonlinear oscillation: an extension of a Bhatia result 1505
144. Oscillation and nonoscillation of a class of neutral equations 1515
145. Positive nonlinear operators associated with isoperimetric eigenvalue problems in algebra 1523
146. Positive nonlinear systems: Some results and applications 1529
147. Random products of contractions 1541
148. Functional-differential equations with non-Volterra operator 1549
149. Searching for periodic orbits in a four dimensional symplectic map 1557
150. Nonlinear Gravito-electrodynamics - An Einstein's dream 1565
151. A geometric approach to optimal control 1579
152. A generalized implicit function theorem for equations with symmetry 1591
153. Bifurcation analysis of nonuniform flow patterns in axial-flow gas compressors 1597
154. Analysis of energy balance climate models 1609
155. A numerical method for solving nonlinear singular problems and application to bifurcation problems 1619
156. On the analysis of dynamic bifurcations and stability of solutions 1627
157. Limit theorems for dependent random variables 1639
158. The stochastic zero-sum differential games with measurement uncertainties 1651
159. On certain nonlinear difference and differential equations arising from optimal choice problems 1663
160. Near-optimal control of a class of stochastic systems under integral constraints 1677
161. Stability analysis of stochastic bilinear systems 1689
162. Existence of solutions of nonlinear stochastic differential inclusions on Banach space 1699
163. Bimodal nonparametric density estimation 1713
164. Conditional percentiles and their estimates for the additive model 1727
165. Sequential allocation for a nonlinear estimation problem 1739
166. Ergodic theorems for modulated stochastic processes 1745
167. Some new results in stochastic reaction-diffusion equations 1757
168. Stochastic evolution equations with non-coercive monotone operators 1765
169. Optimal control of arrival and service rates for two Μ / Μ / 1 queues in series 1779
170. Repairable system with different failure modes 1785
171. Differential inclusions and implicit equations on closed subsets of ℝn 1797
172. Recent trends in the theory of nonlinear functional differential equations 1807
173. Spherically symmetric solutions of semilinear wave equations 1815
174. Exchange of stability and bifurcation of tori in four dimensions 1819
175. Multivalued differential equations with time-dependent constraints 1829
176. Weighted inequalities with an arbitrary convex function 1841
177. Lower semicontinuity of multivalued mappings and equilibrium points 1849
178. Periodicity in delay difference systems 1861
179. A convexification algorithm for the modeling of nonlinear dynamic processes 1871
180. On the pulse phenomenon for impulsive differential equations 1881
181. Fourier spectral methods for a class of generalized KdV-Burgers equations with variable coefficients 1887
182. Structure of elastoplastic shock wave and numerical computation 1899
183. Automatic contours detection in image processing 1911
184. Second generation image coding and wavelet transform 1923
185. Segmentation by minimizing functionals and the merging methods 1933
186. Equivalence of various characterizations of the oscillatory / nonoscillatory classification for singular endpoints of fourth order selfadjoint differential equations 1943
187. Taylor recurrence in analytic O.D.E.'s 1955
188. Asymptotic behavior of difference equations 1967
189. Oscillation of solutions of arbitrary order neutral functional differential equations with forcing terms 1977
190. Method of Lyapunov-Lagrange functions for optimization of dynamic systems with information constraints 1989
191. Approximation methods for eigenvalue problems of Fredholm integral equations 2001
192. Mode interaction at a triple zero point of O(2)-symmetric nonlinear systems with two parameters 2011
193. Author Index 2023
194. Nonlinear elliptic systems arising from control theory and differential games 2029
195. Aspects of singular perturbation theory in physiology 2045
196. Quasi-variational systems 2055
197. New spectral representations of mixing dynamical systems 2069
198. Differential inclusions without convexity: A survey of directionally continuous selections 2081
199. Some problems of existence, uniqueness and regularity in the calculus of variations 2089
200. On the existence problem in the Calculus of Variations 2097
201. A class of upper semicontinuous differential inclusions without convexity 2107
202. Constructive aspects of fixed point theory for nonexpansive mappings 2115
203. On the growth properties of the homology of free loop spaces on configuration spaces 2127
204. Borsuk-Ulam theorems, the Lusternik-Schnirelmann category and index theories 2135
205. Monotone methods with applications to nonlinear analysis 2147
206. Spherical algorithms and evaluation of the fixed point set 2159
207. Fixed points of acyclic maps on topological vector spaces 2171
208. Convergence of Accretive Operators 2179
209. Existence of solutions of nonlinear equations with perturbations of monotone operators in reflexive Banach spaces 2187
210. Recent results involving compact perturbations and compact resolvents of accretive operators in Banach spaces 2197
211. Braess's paradox and power-law nonlinearities in networks II 2223
212. On the invertibility of I ± exp(—tA), t >0, with A maximal monotone 2231
213. A global existence theorem on nonlinear evolution equations 2239
214. Existence of solutions of nonlinear functional differential equations in Lp spaces 2249
215. The global attractor of the fifth order KdV equation 2261
216. On the blow-up of solutions to some semilinear parabolic systems arising in chemical reaction modelling 2273
217. Asymptotic behavior and periodic forcing in time for the solutions of a nonlinear system representing a phase change with dissipation 2281
218. Implicit functions defined by generalized equations 2289
219. Non-smooth sub differentials: their calculus and applications 2299
220. Generalized differentiation and stability of solution maps to parametric variational systems 2311
221. The linear nonconvex generalized gradient 2325
222. Second order necessary conditions for nonsmooth optimum problems with constraints 2337
223. Wellposedness of second-order nonlinear abstract differential equations with multivalued boundary conditions: Applications to von Kármán systems 2347
224. Some stability results for vector optimization problems in partially ordered topological vector spaces 2371
225. Some nonlinear results for abstract differential equations 2383
226. Some applications and extensions of P-coercive variational inequalities 2391
227. On semilinear wave equations at resonance 2399
228. Approximate solvability of nonlinear equations and related results in control theory 2409
229. The Newton-Kantorovich method for nonlinear integral operators 2419
230. A uniqueness theorem for a nonlinear integral equation of gravimetry 2423
231. Applications of Pareto optimality of a mapping to mathematical economics 2431
232. On ψ-minimal, P-monotone trajectories of nonautonomous differential inclusion in ℝN 2441
233. On the solution of some nonlinear boundary value problem 2449
234. Mathematical controllability theory of the growth of wealth of nations 2459
235. Bilateral interactions and aggregate fluctuations 2471
236. Short-run decisions on price, output, and inventories in a dynamic model of the firm 2481
237. Dynamical systems defined by infinite horizon optimal control problems 2493
238. Geometry and nonlinear differential equations 2503
239. Pareto solution of a cone variational inequality and Pareto optimality of a mapping 2511
240. Output tracking of nonanalytic trajectories for nonlinear systems 2521
241. Linearization and approximation of control systems 2531
242. The shape design problem for systems with distributed parameters 2541
243. Optimality conditions for controls of infinite dimensional systems 2549
244. Two norm approach in stability analysis of optimization and optimal control problems 2557
245. On nonlinear minimum norm control problems 2569
246. Generalizations of the Lusternik Theorem and applications to nonsmooth and abnormal problems in optimization and optimal control 2583
247. Optimal shape design of plates and shells with obstacles 2595
248. Some results on the viscosity solutions of fully nonlinear equations containing non-local terms 2605
249. Optimal control and relaxation of systems governed by Volterra integral equations 2617
250. A universal stabilizer for a class of nonlinear systems 2633
251. Computational methods for boundary optimal control of incompressible flows 2643
252. Computational hybrid-control techniques in hydrodynamics 2655
253. Optimal control problems of viscous flow 2667
254. A direct method for parameter estimation in distributed systems 2679
255. Uniformly stable approximation of the LQR problem 2687
256. On a mathematical model of phase transitions in materials with memory 2697
257. Overview of optimal trajectories for aeroassisted orbital transfer 2705
258. Long term planning of hydro-thermal power systems 2723
259. On the optimal drug administration of a discrete cancer chemotherapy model 2735
260. The neural network approach to several nonlinear control problems 2749
261. A unified computational approach to optimal control problems 2763
262. Some trajectory-following algorithms for min-max optimization 2775
263. On the usage and applications of parameter optimization software OptiA in constrained optimal control 2779
264. Construction of numerical solutions of permanent heavy waves of two liquids 2791
265. Asymptotic theorems about compression and expansion of cones in Banach spaces for multivalued maps differentiable at the origin and infinity 2803
266. Bayesian statistical approach to design of reliability models 2815
267. Determine optimal burn-in time for highly integrated circuit systems 2827
268. A nonhomogeneous Poisson process for software reliability 2837
269. Multiple category screening procedures 2851
270. Is your model chaotic? A consistent simulation-based test 2861
271. Economic models of survival under uncertainty 2873
272. Aggregation in mathematical models of manufacturing systems 2885
273. Nonlinear interaction dynamics of multiple mobile automata 2897
274. Some unsolved problems in optimal design theory: Interaction of mathematical modelling of large structural, mechanical or chemical systems with their design 2909
275. Stochastic stability and bifurcation analysis of gated radar trackers 2931
276. The twist-and-flip map 2943
277. Bifurcations and chaos from Chua's circuit: A state-of-the-art review 2957
278. Nonlinear dynamics in cellular neural networks 2969
279. CNN: A new paradigm of nonlinear dynamics in space 2979
280. Geometric invariants of chaotic attractors encountered in Chua's circuit 2991
281. Nonstandard methods in metric fixed point theory 3003
282. The minimax principle of mechanics and its application to the optimal control problem for robot manipulators 3013
283. On a fixed point theorem of Jungck 3019
284. A nonlinear ergodic theorem for almost-orbits of nonlinear contraction semigroups in Banach spaces 3025
285. Author Index 3037
286. A simple ODE with more than 20 strange attractors 3043
287. Applications of generalized functions to propagating and deforming interfaces 3055
288. Conservation laws for integro-differential equations 3069
289. Dynamics of neuro-muscular control with delayed displacement-dependent feedback 3085
290. Oscillations and chaos in nonlinear delay differential equations with applications to physiology 3095
291. Multiple-delayed differential equations as models for biological control systems 3109
292. Lattices with spatially extended coupling and the statistical properties of neural populations 3119
293. Dependence on initial conditions in nonlocal PDE's and hereditary dynamical systems 3125
294. Biased preference models for partnership formation 3137
295. AIDS in the Heterosexual Population 3149
296. Completion of mixing matrices for non-closed social networks 3163
297. Modelling vector-host disease transmission and food web dynamics through the mixing/pair formation approach 3175
298. Simple models for interactions of the HIV virus and the immune system: Can we point out to one specific threshold for the onset of AIDS? 3187
299. Variable infectivity in communicable disease models 3201
300. Stochastic and deterministic models in epidemiology 3211
301. A pair formation approach to modeling inheritance of social traits 3227
302. Information processing and practical implementation of “Biochemical neuron” 3235
303. Nonlinear control and self-organization 3245
304. Analysis of two hypothetical mechanisms of photosynthetic oscillations by means of mathematical skeleton models 3255
305. The theory of the control of metabolism 3267
306. Mathematical modelling of enzymic systems; simulation, control analysis and optimization 3277
307. Selection of enzymatic mechanisms which account for simplicity in the evolution of metabolic pathways 3291
308. Mathematical description of regulation in metabolic systems: The regulatory potential 3305
309. Self-activation and self-inactivation kinetics of enzymes: theoretical aspects and a mathematical model for the particulate prostaglandine synthase from ovine vesicular glands 3311
310. Power-law formalism: A canonical nonlinear approach to modeling and analysis 3323
311. S-system analysis of the TCA cycle in Dictyostelium discoideum 3335
312. A monomial-based version of Newton's method 3347
313. Assessment of the regulatory properties of a metabolic pathway: Parameter estimation from steady-state measurements 3357
314. How many variables? Some comments on the dimensionality of nonlinear systems 3369
315. Simple dynamical systems for bursting and spindling 3381
316. A two-component discrete dynamical model of the bursting rhythm caused by veratramine in the pacemaker of the heart 3389
317. On the clonal inheritance model of cell proliferation 3401
318. Emergence of stable DNA repeats from random sequences under unequal sister chromatid exchange 3409
319. A model for retrieving the dynamics of gene amplification from episomes to intrachromosomal amplification 3419
320. New mathematical methods for evaluating toxicity of anti-cancer drugs and AZT 3433
321. A particle method for population shock waves with application to synchronization of bacterial culture growth 3443
322. Simulation of drug-inhibited cell proliferation with a model of clonal inheritance of cell lifetimes 3455
323. Resonances in periodic chemotherapy scheduling 3463
324. A review of the effect of radiation transfer on the simulation of atmospheric circulations of different scales 3475
325. Effects of thermal forcing in atmospheric shear flows with critical level 3491
326. Baroclinic-barotropic instabilities and energy transfers in the Gulf Stream 3515
327. Turbulence structure in the atmospheric boundary layer – data and models 3533
328. A review of coupled ocean-atmosphere models 3545
329. Review of recent advances in the development of semi-Lagrangian numerical models in meteorology 3559
330. Atmospheric dispersion in low wind conditions 3567
331. A review of non-hydrostatic numerical models for the atmosphere 3595
332. The stagnant flow upstream of hills or mountains 3611
333. Micro-meteorological studies in air quality management 3619
334. Nonlinear analysis of stability, oscillations and control of immunological processes 3633
335. Mathematical modeling of cellular interaction dynamics in multicellular tumor spheroids 3645
336. Polynomial networks for optimal nonlinear filtering 3655
337. Analysis of the computational characteristics of adaptive resonance theory neural nets 3669
338. Differentiating and pruning multilayer feedforward neural networks 3681
339. Stability analysis of neural networks using vector Lyapunov functions 3695
340. Neural network approach to optimal filtering 3705
341. Signal recognition using a dynamic time warping neural network 3717
342. Development and analysis of a mathematical model for a plant-herbivore system 3723
343. The effects of asymmetric competition on competitive outcome 3733
344. Persistence in Kolmogorov population models with time delay 3741
345. Global variables and population dynamics prey-predator models with individual activity sequences 3753
346. The computer-aided study of dynamics in the system primary tumor, cytotoxic lymphocytes, metastases 3763
347. Folding at the genesis of chaos 3765
348. Ginzburg-Landau type models for superconductivity 3779
349. Time-dependent Ginzburg-Landau models for superconductivity 3789
350. Asymptotic analysis of the Ginzburg-Landau model of superconductivity: Reduction to a free boundary model 3803
351. Dynamics of Vortices in Superconductors 3811
352. Computation of Singular Solutions in the Micromagnetics of Thin Films 3823
353. Energy transport systems for semiconductors: Analysis and simulation 3835
354. Nonlinearities In Drift-Diffusion Semiconductor Modeling 3847
355. Some classes of iterative methods for finding zeros of polynomials and analytic functions 3859
356. Fine and coarse grained parallel implementations of polynomial root finding algorithms 3871
357. Divide and conquer techniques for the polynomial root-finding problem 3885
358. A unified approach to some classes of simultaneous inclusion methods for polynomial zeros 3897
359. WKB procedure for Schrödinger type difference equations 3907
360. Toward an efficient and stable determination of spectra of a general matrix and a more efficient solution of the Lyapunov equation 3913
361. Interfacial wave theory of dendritic growth and a comparison with experiments 3929
362. Thomas–Fermi model calculations of one and two dimensional lattices 3941
363. Author Index 3949