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

Title & Authors
OSCILLATORY BEHAVIOR OF A CERTAIN CLASS OF SECOND-ORDER NONLINEAR PERTURBED DYNAMIC EQUATIONS ON TIME SCALES
Saker, Samir H.;

Abstract
This paper is concerned with the asymptotic behavior of solutions of the second-order nonlinear perturbed dynamic equation $\small{(r(t)x^{\Delta}(t))^{\Delta}\;+\;F(t,\;x^{\sigma}))=G(t,\;x^{\sigma},\;(x^{\Delta})^{\sigma})}$ on a time scale $\small{\mathbb{T}}$. 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;
Language
English
Cited by
1.
On the oscillation for third-order nonlinear neutral delay dynamic equations on time scales, Journal of Applied Mathematics and Computing, 2017, 54, 1-2, 243
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