Existence of generalized, positive and periodic solutions for some differential equations of order II

Abstract

We study the existence of positive periodic solutions of the equations y00(x) − P0(x)y(x) + μQ0(x)f(x, y(x)) = 0, y00(x) + P0(x)y(x) = μQ0(x)f(x, y(x)), where μ > 0, P and Q are real nondecreasing functions, P0 and Q0 are 1- periodic distributions, f is a continuous function and 1-periodic in the first variable. The Krasnosielski fixed point theorem on cone is used.