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), x'(t), . . . , x(n−1)(t)) = 0,
x(n)(t) + p(t)x(t) = μf(t, x(t), x'(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.
Keywords
positive solutions; boundary value problems; cone; Krasnosielski fixed point theorem; Green’s function
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Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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