Existence of positive periodic solutions of some differential equations of order n (n>2)

Abstract

We study the existence of positive periodic solutions of the equations x(n)(t) − p(t)x(t) + μf(t, x(t), x0(t), . . . , x(n−1)(t)) = 0, x(n)(t) + p(t)x(t) = μf(t, x(t), x0(t), . . . , x(n−1)(t)), where n >= 2, μ > 0, p: (−∞,∞) -> (0, ∞) is continuous and 1–periodic, f is a continuous function and 1–periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used.