Existence of positive periodic solutions for two types of second-order nonlinear neutral differential equations with infinite distributed delay

Abstract

In this article we study the existence of positive periodic solutions for two types of second-order nonlinear neutral differential equation with infinite distributed delay. The main tool employed here is the Krasnoselskii’s fixed point theorem dealing with a sum of two mappings, one is a contraction and the other is completely continuous. The results obtained here generalize the work of Han and Ren (Nonlinear Anal, 70:1393–1406, 2009).