Existence of positive quasi-homoclinic solutions for damped p-Laplacian differential equations
by Monia Boujlida
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 10, No. 6, 2020

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.

Online publication date: Tue, 02-Feb-2021

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