Abstract
The oscillatory and asymptotic behavior results for a class of third-order nonlinear neutral dynamic equations on time scales are presented. The results obtained can be extended to more general third-order neutral dynamic equations of the type considered here. Examples are provided to illustrate the applicability of the results.
Highlights
1 Introduction This work is concerned with oscillation and asymptotic behavior of solutions to a thirdorder nonlinear neutral dynamic equation r(t) x(t) + p(t)x g(t)
On an arbitrary time scale T, where α is a quotient of odd positive integers
Since we are interested in the oscillation and asymptotic behavior of solutions for large t, we assume that sup T = ∞ and define the time scale interval [t, ∞)T by [t, ∞)T := [t, ∞) ∩ T with t ∈ T
Summary
Since we are interested in the oscillation and asymptotic behavior of solutions for large t, we assume that sup T = ∞ and define the time scale interval [t , ∞)T by [t , ∞)T := [t , ∞) ∩ T with t ∈ T. There has been much research activity concerning the oscillation of solutions of various functional differential equations and functional dynamic equations on time scales, and we refer the reader to the papers [ – ] and the references therein as examples of recent results on this topic. It becomes apparent that results on the oscillatory and asymptotic behavior of third-order neutral dynamic equations on time scales are relatively scarce and most such results are concerned with the cases where ≤ p(t) < p < , – ≤ p(t) < , and/or ≤
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