Abstract
We study the existence of nonoscillatory solutions tending to zero of a class of third-order nonlinear neutral dynamic equations on time scales by employing Krasnoselskii’s fixed point theorem. Two examples are given to illustrate the significance of the conclusions.
Highlights
1 Introduction In this paper, we consider the existence of nonoscillatory solutions tending to zero of a class of third-order nonlinear neutral dynamic equations r1(t) r2(t) x(t) + p(t)x g(t)
Zhu and Wang [17] were concerned with a first-order neutral dynamic equation x(t) + p(t)x g(t) + f t, x h(t) = 0
It is not easy to find a necessary condition for equations to have a nonoscillatory solution tending to zero asymptotically
Summary
1 Introduction In this paper, we consider the existence of nonoscillatory solutions tending to zero of a class of third-order nonlinear neutral dynamic equations r1(t) r2(t) x(t) + p(t)x g(t) The existence of nonoscillatory solutions of neutral dynamic equations on time scales has been studied successively in [6, 7, 11, 13,14,15,16,17]. Similar sufficient conditions for the existence of nonoscillatory solutions tending to zero of neutral dynamic equations have been presented.
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