[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2010.47.4.659

OSCILLATORY BEHAVIOR OF A CERTAIN CLASS OF SECOND-ORDER NONLINEAR PERTURBED DYNAMIC EQUATIONS ON TIME SCALES

Saker, Samir H. (DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCE KING SAUD UNIVERSITY, DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE MANSOURA UNIVERSITY)

Publication Information

Journal of the Korean Mathematical Society / v.47, no.4, 2010 , pp. 659-674 More about this Journal

Abstract

This paper is concerned with the asymptotic behavior of solutions of the second-order nonlinear perturbed dynamic equation $(r(t)x^{\Delta}(t))^{\Delta}\;+\;F(t,\;x^{\sigma}))=G(t,\;x^{\sigma},\;(x^{\Delta})^{\sigma})$ on a time scale $\mathbb{T}$ . By using a new technique we establish some sufficient conditions which ensure that every solution oscillates or converges to zero. Our results improve the known oscillation results on the literature for the perturbed dynamic equations on time scales. Some examples illustrating our main results are given.

Keywords

oscillation; perturbed dynamic equations; time scale;

Citations & Related Records

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