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
y''(x) - P'(x)y(x) + μQ'(x)f(x,y(x)) = 0,
y''(x) + P'(x)y(x) = μQ'(x)f(x,y(x)),
where μ>0, P and Q are real nondecreasing functions, P' and Q' 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.
Keywords
positive; periodic solutions; cone; distributions; Krasnosielski fixed point theorem; Green function
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Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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