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

Jan Ligęza

Published: 2009-09-30

Vol. 23 (2009)

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

Jan Ligęza

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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Ligęza, J. (2009). Existence of positive periodic solutions of some differential equations of order n (n≥2). Annales Mathematicae Silesianae, 23, 61–81. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14045

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Vol. 23 (2009)
Published: 2009-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

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