On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
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Said R. Grace
,
John R. Graef
Abstract
New oscillation criteria for certain third order nonlinear dynamic equations with a nonlinear damping term are established. Examples to illustrate the results are included.
References
[1] Bohner, M.—Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.10.1007/978-1-4612-0201-1Suche in Google Scholar
[2] Chen, D.-X.—Liu, J.-C.: Asymptotic behavior and oscillation of solutions of third-order nonlinear neutral delay dynamic equations on time scales, Can. Appl. Math. Q. 16 (2008), 19–43.Suche in Google Scholar
[3] Elabbasy, E. M.—Hassan, T. S.: Oscillation of solutions for third order functional dynamic equations, Electron. J. Differential Equations 2010 (2010), No. 131, 14 pp.Suche in Google Scholar
[4] Erbe, L.—Hassan, T. S.—Peterson, A.: Oscillation of third order functional dynamic equations with mixed arguments on time scales, J. Appl. Math. Comput. 34 (2010), 353–371.10.1007/s12190-009-0326-6Suche in Google Scholar
[5] Erbe, L.—Hassan, T. S.—Peterson, A.: Oscillation of third order nonlinear functional dynamic equations on time scales, Differ. Equ. Dyn. Syst. 18 (2010), 199–227.10.1007/s12591-010-0005-ySuche in Google Scholar
[6] Erbe, L.—Peterson, A.—Saker, S. H.: Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation, Can. Appl. Math. Q. 14 (2006), 129–147.Suche in Google Scholar
[7] Erbe, L.—Peterson, A.—Saker, S. H.: Hille and Nehari type criteria for third-order dynamic equations, J. Math. Anal. Appl. 329 (2007), 112–131.10.1016/j.jmaa.2006.06.033Suche in Google Scholar
[8] Grace, S. R.: On the oscillation of nth order dynamic equations on time-scales, Mediterr. J. Math. 10 (2013), 147–156.10.1007/s00009-012-0201-9Suche in Google Scholar
[9] Grace, S. R.—Agarwal, R. P.—Bohner, M.—O’Regan, D.: Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009), 3463–3471.10.1016/j.cnsns.2009.01.003Suche in Google Scholar
[10] Grace, S. R.—Agarwal, R. P.—Zafer, A.: Oscillation of higher order nonlinear dynamic equations on time scales, Advances in Diff. Eqns. 67 (2012), 1–18.10.1186/1687-1847-2012-67Suche in Google Scholar
[11] Grace, S. R.—Bohner, M.—Agarwal, R. P.: On the oscillation of second-order half-linear dynamic equations, J. Differ. Eqs. Appl. 15 (2009), 451–460.10.1080/10236190802125371Suche in Google Scholar
[12] Grace, S. R.—Graef, J. R.—El-Beltagy, M. A.: On the oscillation of third order neutral delay dynamic equations on time scales, Comput. Math. Appl. 63 (2012), 775–782.10.1016/j.camwa.2011.11.042Suche in Google Scholar
[13] Grace, S. R.—Hassan, T. S.: Oscillation criteria for higher order nonlinear dynamic equations, Math. Nachr. 287 (2014), 1659–1673.10.1002/mana.201300157Suche in Google Scholar
[14] Han, Z.—Li, T.—Sun, S.—Cao F.: Oscillation criteria for third order nonlinear delay dynamic equations on time scales, Ann. Polon. Math. 99 (2010), 143–156.10.4064/ap99-2-3Suche in Google Scholar
[15] Han, Z.—Li, T.—Sun, S.—Zhang, C.: Oscillation behavior of third-order neutral Emden-Fowler delay dynamic equations on time scales, Adv. Differ. Equ. 2010 (2010), Article ID 586312, 23 pages.10.1186/1687-1847-2010-586312Suche in Google Scholar
[16] Han, Z.—Li, T.—Sun, S.—Zhang, M.: Oscillation behavior of solutions of third-order nonlinear delay dynamic equations on time scales, Commun. Korean Math. Soc. 26 (2011), 499–513.10.4134/CKMS.2011.26.3.499Suche in Google Scholar
[17] Hassan, T. S.: Oscillation of third order nonlinear delay dynamic equations on time scales, Math. Comput. Modelling 49 (2009), 1573–1586.10.1016/j.mcm.2008.12.011Suche in Google Scholar
[18] Ji, T.—Tang, S.—Li, T.: Corrigendum to “Oscillation behavior of third-order neutral Emden-Fowler delay xdynamic equations on time scales” Adv. Difference Equ. 2012 (2012), 4 pp.10.1186/1687-1847-2012-57Suche in Google Scholar
[19] Jia, B.: Forced oscillation of third order nonlinear dynamic equations on time scales, Ann. Polon. Math. 99 (2010), 79–87.10.4064/ap99-1-7Suche in Google Scholar
[20] Li, T.—Han, Z.—Sun, S.—Zhao, Y.: Oscillation results for third order nonlinear delay dynamic equations on time scales, Bull. Malays. Math. Sci. Soc. 34 (2011), 639–648.Suche in Google Scholar
[21] Li, T.—Han, Z.—Sun, S.—Zhao, Y.: Asymptotic behavior of solutions for third-order half-linear delay dynamic equations on time scales, J. Appl. Math. Comput. 36 (2011), 333–346.10.1007/s12190-010-0406-7Suche in Google Scholar
[22] Li, T.—Han, Z.—Zhang, C.—Sun, Y.: Oscillation criteria for third-order nonlinear delay dynamic equations on time scales, Bull. Math. Anal. Appl. 3 (2011), 52–60.Suche in Google Scholar
[23] Saker, S. H.: On oscillation of a certain class of third-order nonlinear functional dynamic equations on time scales, Bull. Math. Soc. Sci. Math. Roumanie (N. S.) 54(102) (2011), 365–389.10.1007/s11425-011-4304-8Suche in Google Scholar
[24] Saker, S. H.: Oscillation of third-order functional dynamic equations on time scales, Sci. China Math. 54 (2011), 2597–2614.10.1007/s11425-011-4304-8Suche in Google Scholar
[25] Saker, S. H.—Graef, J. R.: Oscillation of third-order nonlinear neutral functional dynamic equations on time scales, Dynam. Systems Appl. 21 (2012), 583–606.Suche in Google Scholar
[26] Sun, Y.—Han, Z.—Sun, Y.—Pan, Y.: Oscillation theorems for certain third order nonlinear delay dynamic equations on time scales, Electron. J. Qual. Theory Differ. Equ. 2011 (2011), No. 75, 14 pp.10.14232/ejqtde.2011.1.75Suche in Google Scholar
[27] Wang, Y.—Xu, Z.: Asymptotic properties of solutions of certain third-order dynamic equations, J. Comput. Appl. Math. 236 (2012), 2354–2366.10.1016/j.cam.2011.11.021Suche in Google Scholar
[28] Zhang, C.—Saker, S. H.—Li, T.: Oscillation of third-order neutral dynamic equations on time scales, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 20 (2013), 333–358.Suche in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
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Artikel in diesem Heft
- 10.1515/ms-2015-0200
- Zero-divisor graphs of lower dismantlable lattices I
- Some results on the intersection graph of submodules of a module
- Class number parities of compositum of quadratic function fields
- Examples of beurling prime systems
-
Connection between multiplication theorem for Bernoulli polynomials and first factor
- On permutational invariance of the metric discrepancy results
- Evaluation of sums containing triple aerated generalized Fibonomial coefficients
- Linear algebraic proof of Wigner theorem and its consequences
- A note on groups with finite conjugacy classes of subnormal subgroups
- Groups with the same complex group algebras as some extensions of psl(2, pn)
- Klee-Phelps convex groupoids
- On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
- Weak interpolation for the lipschitz class
- Generalized Padé approximants for plane condenser and distribution of points
- Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
- Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
- Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
- Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
- On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
- Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
- Semi-equivelar maps on the torus and the Klein bottle with few vertices
- A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
