On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations
-
Aurel Diamandescu
Abstract
The paper provides (necessary and) sufficient conditions for Ψ-strong stability of the trivial solution of a linear Lyapunov matrix differential equations. Further, sufficient condition are obtained for Ψ-strong stability of the trivial solution of a nonlinear Lyapunov matrix differential equation.
References
[1] ASCOLI, G.: Osservazioni sopre alcune questioni di stabilita, I, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 9 (1950), 129-134.Suche in Google Scholar
[2] BELLMAN, R.: Introduction to Matrix Analysis, McGraw-Hill Book Company, Inc., New York, 1960.Suche in Google Scholar
[3] COPPEL, W. A.: Stability and Asymptotic Behavior of Differential Equations, D. C. Heath and Company, Boston, 1965.Suche in Google Scholar
[4] DIAMANDESCU, A.: On the strong stability of a nonlinear Volterra integro-differential system, Acta Math. Univ. Comenian. (N.S.) LXXV (2006), 153-162.Suche in Google Scholar
[5] DIAMANDESCU, A.: Ψ-bounded solutions for a Lyapunov matrix differential equation, Electron. J. Qual. Theory Differ. Equ. 2009 (2009), No. 17, 1-11.Suche in Google Scholar
[6] DIAMANDESCU, A.: On Ψ-stability of a nonlinear Lyapunov matrix differential equations, Electron. J. Qual. Theory Differ. Equ. 2009 (2009), No. 54, 1-18.Suche in Google Scholar
[7] DIAMANDESCU, A.: On Ψ-asymptotic stability of nonlinear Lyapunov matrix differential equations, An. Univ. Vest Timi，s. Ser. Mat.-Inform. L, (2012), 3-25.10.2478/v10324-012-0001-8Suche in Google Scholar
[8] DIAMANDESCU, A.: On the Ψ-instability of nonlinear Lyapunov matrix differential equations, An. Univ. Vest Timi，s. Ser. Mat.-Inform. XLIX (2011), 21-37.Suche in Google Scholar
[9] MURTY,M. S. N.-SURESH KUMAR,G.: On Ψ-boundedness and Ψ-stability of matrix Lyapunov systems, J. Appl. Math. Comput. 2008 (2008), No. 26, 67-84.Suche in Google Scholar
[10] MURTY, M. S. N.-SURESH KUMAR,G.: On dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, J. Korean Math. Soc. 45 (2008), 1361-1378.10.4134/JKMS.2008.45.5.1361Suche in Google Scholar
[11] MURTY, M. S. N.-KUMAR, G. S.-LAKSHMI, P. N.-ANJANEYULU, D.: On Ψ-instability of non-linear matrix Lyapunov systems, Demonstratio Math. XLII (2009), 731-743.10.1515/dema-2013-0211Suche in Google Scholar
[12] MURTY, M. S. N.-SURESH KUMAR, G.-ANJANEYULU, D.: On Ψ-strong stability of non-linear Volterra integro-diferential systems, Mathematical Sciences Quarterly 3 (2009), 25-40.Suche in Google Scholar
[13] WINTNER, A.: Asymptotic integrations of the adiabatic oscillator, Amer. J. Math. 69 (1947), 251-272.10.2307/2371850Suche in Google Scholar
© Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Fuzzy Pseudo Subalgebras and Ideals of Pseudo D-Algebras
- Five Curious Congruences Modulo p2
- On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums
- Constructing New Crossed Group Categories Over Weak Hopf Group Algebras
- Generalization of Hilbert Inequality with Some Parameters
- Some Applications of Differential Subordination of p-Valent Functions
- Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions
- On Properties of Entire Solutions of Difference Equations and Difference Polynomials
- On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations
- On the Existence of Solutions of Ordinary Differential Equations in Banach Spaces
- Global Dynamics of a Delayed n + m-Species Competition Predator-Prey System on Time Scales
- Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System
- A Generalization of Cyclic Amenability of Banach Algebras
- n-Weak Module Amenability of Triangular Banach Algebras
- On a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space
- Optimality Conditions for Vector Equilibrium Problems with Set-Valued Mappings and Cone Constraints
- Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms
- A New Proof of a Theorem on Long Cycles
Artikel in diesem Heft
- Fuzzy Pseudo Subalgebras and Ideals of Pseudo D-Algebras
- Five Curious Congruences Modulo p2
- On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums
- Constructing New Crossed Group Categories Over Weak Hopf Group Algebras
- Generalization of Hilbert Inequality with Some Parameters
- Some Applications of Differential Subordination of p-Valent Functions
- Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions
- On Properties of Entire Solutions of Difference Equations and Difference Polynomials
- On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations
- On the Existence of Solutions of Ordinary Differential Equations in Banach Spaces
- Global Dynamics of a Delayed n + m-Species Competition Predator-Prey System on Time Scales
- Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System
- A Generalization of Cyclic Amenability of Banach Algebras
- n-Weak Module Amenability of Triangular Banach Algebras
- On a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space
- Optimality Conditions for Vector Equilibrium Problems with Set-Valued Mappings and Cone Constraints
- Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms
- A New Proof of a Theorem on Long Cycles
