Existence and uniqueness of positive even homoclinic solutions for second order differential equations

Daouas, Adel and Boujlida, Monia: Existence and uniqueness of positive even homoclinic solutions for second order differential equations. Electronic journal of qualitative theory of differential equations 45. pp. 1-12. (2019)

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Abstract

This paper is concerned with the existence of positive even homoclinic solutions for the p-Laplacian equation (|u 0 p−2u 0 0 − a(t)|u| p−2u + f(t, u) = 0, t ∈ R, where p ≥ 2 and the functions a and f satisfy some reasonable conditions. Using the Mountain Pass Theorem, we obtain the existence of a positive even homoclinic solution. In case p = 2, the solution obtained is unique under a condition of monotonicity on the function u 7−→ f(t,u) u . Some known results in the literature are generalized and significantly improved.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 45
Page Range: pp. 1-12
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.45
Uncontrolled Keywords: Másodrendű differenciálegyenlet
Additional Information: Bibliogr.: p. 10-12. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 30. 07:44
Last Modified: 2019. Sep. 30. 09:41
URI: http://acta.bibl.u-szeged.hu/id/eprint/62123

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