This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. We give the necessary and sufficient conditions guaranteeing the existence of bounded nonoscillatory solutions. Sufficient conditions are proved via a topological approach based on the Banach fixed point theorem.
MSC: 34C10
Keywords
ABSTRACT. The aim of this paper is to present some results concerning with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the necessary and sufficient conditions ensuring the existence of nonoscillatory solutions tending to zero as t → ∞.
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.
The aim of this paper is to study the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the sufficient conditions ensuring the existence of some nonoscillatory solutions with a specified asymptotic property as t tends to infinity. The basic tool used in proving our results is the classical Banach contraction mapping principle.
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