Positive periodic solutions to impulsive delay differentialequations

Abstract

In this paper we discuss the existence of positive periodic solutions for nonautonomous second order delay differential equations with singular nonlinearities in the presence of impulsive effects. Simple sufficient conditions are provided that enable us to obtain positive periodic solutions. Our approach is based on a variational method.

Positive periodic solutions for a class of second-order differential equations with state-dependent delays

“…In this paper, based on some recent work on positivity of solotions [6,7,15] and by virtue of some properties of a Green's function, some recent results such as those obtained in [3,5,11,14,18] and a Krasnoselskii fixed point theorem, we investigate the existence and positivity of periodic solutions for the following class of second order iterative differential equations: [2] (t), ..., x [n] (t) +…”