Abstract
Using Lyapunov-Krasovskii functional approach, we establish a new result to guarantee the existence of periodic solutions of a certain multidelay nonlinear functional differential equation of second order. By this work, we extend and improve some earlier result in the literature.
Highlights
It is well known that the problem of the existence of periodic solutions of retarded functional differential equations of second order is very important in the background applications, and of considerable significance in theory of differential equations
By using the famous continuation theorem of degree theory, many authors have made a lot of interesting contributions to the topic for retarded functional differential equations of second order
In the same paper, the authors applied the following Theorem A to discuss the existence of an ω-periodic solution of the nonlinear delay differential equation of the second order: x (t) + ax (t) + g (x (t − τ)) = p (t), (1)
Summary
It is well known that the problem of the existence of periodic solutions of retarded functional differential equations of second order is very important in the background applications, and of considerable significance in theory of differential equations. The motivation of this paper is that in recent years the study of the existence of periodic solutions to various kinds of retarded functional differential equations of second order has become one of the most attractive topics in the literature.
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