Existence of solutions for nonlinear p-Laplacian diference equations

2016/06/24 by Lorena Saavedra, Saavedra, L., Stepan Tersian +1
Engineering · Mathematics · #39A12 #47J30 #58E05 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1606.07607

openalex publication_date 2016/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is the study of existence of solutions for non- linear p-Laplacian difference equations. In the first part, the existence of a nontrivial homoclinic solution for a discrete p-Laplacian problem is proved. The proof is based on the mountain-pass theorem of Brezis and Nirenberg. Then, we study the existence of multiple solutions for a discrete p-Laplacian boundary value problem. In this case the proof is based on the theorem of D. Averna and G. Bonanno, which ensures the existence of three critical points for a suitable functional.

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