On homoclinic solutions for a second order difference equation with p-Laplacian

2016/03/24 by Robert Stegliński, Stegliński, Robert
Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1603.07522

arXiv admin note: text overlap with arXiv:1603.07104

openalex publication_date 2016/03/24 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain conditions under which the difference equation -Δ( a(k)ϕ_p(Δu(k-1))) +b(k)ϕ_p(u(k))=λf(k,u(k)), k∈ ℤ, has infinitely many homoclinic solutions. A variant of the fountain theorem is utilized in the proof of our theorem. It improves the results in [L.Kong, homoclinic solutions for a second order difference equation with p-Laplacian, Appl. Math. Comput., 247 (2014), 1113--1121], where the set of conditions imposed on nonlinearity is inconsistent.

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