Title: Existence of positive quasi-homoclinic solutions for damped p-Laplacian differential equations

Authors: Monia Boujlida

Addresses: Department of Mathematics, High School of Sciences and Technology, 4011 Hammam Sousse, Tunisia

Abstract: In this paper we prove the existence of nontrivial quasi-homoclinic solutions for the damped p-Laplacian differential equation (|u′|p−2u′)′ + c|u′|p−2u′ − a(t)|u|p−2u + f(t, u) = 0, t ∈ R, where p ≥ 2, c ≥ 0 is a constant and the functions a and f are continuous and not necessarily periodic in t. Using the Mountain-Pass Theorem, we obtain the existence of positive homoclinic solution in both cases sub-quadratic and super-quadratic.

Keywords: quasi-homoclinic solution; the (PS)-condition; mountain pass theorem; damped p-Laplacian differential equation.

DOI: 10.1504/IJDSDE.2020.112757

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.6, pp.493 - 510

Received: 02 Aug 2018
Accepted: 09 Mar 2019

Published online: 21 Jan 2021 *

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