On some classes of nonoscillatory solutions of third-order nonlinear differential equations

Abstract

In this paper, we are concerned with the asymptotic behavior of certain solutions of third-order nonlinear differential equations with quasiderivatives. More precisely, the necessary and sufficient conditions for the existence of some types of nonoscillatory solutions with a specified asymptotic property as t → ∞ are given. In order to prove some of our results, we use a topological approach based on the Banach fixed point theorem.