Multiplicity of solutions to discrete inclusions with the \(p(k)\)-Laplace type equations
type: Item
instance of: scholarly article
title: Multiplicity of solutions to discrete inclusions with the \(p(k)\)-Laplace type equations
zbMATH Open document ID: 1475.35222
author: Malick Zoungrana
author: Stanislas Ouaro
published in: Nonautonomous Dynamical Systems
publication date: 2018-06-06T00:00:00Z
review text: This paper is concerned with the existence and multiplicity of solutions to discrete inclusions with the \(p(k)\)-Laplace type equations. They begin by giving some basic definitions and preliminary results where they define the generalized gradient of a function, coercive and anti-coercive function. Then they introduce three critical points theorem for locally Lipschitz functionals. With this theorem, the authors prove the existence of three \(m\)-periodic solutions and show that at least two of which are non-trivial. For this, they define a functional \(J_m\) by \[ J_{m}(u) = \sum_{k=1}^{m}A\big(k-1,\Delta u(k-1)\big) - \lambda \sum_{k=1}^{m}F\big(k,u(k)\big) \] and establish that a critical point of \(J_m\) is a solution of there equations. By using three critical points theorem, they show that the problem has at least three solutions, at least two of which are necessarily non-zero.
reviewed by: Blaise Koné
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 35B38
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34L30
zbMATH DE Number: 6881274
zbMATH Keywords: \(p(k)\)-Laplace
zbMATH Keywords: multiple solutions
zbMATH Keywords: discrete inclusions
zbMATH Keywords: three critical points theorem
zbMATH Keywords: locally Lipschitz continuous functions
MaRDI profile type: Publication
full work available at URL: msds-2018-0006
OpenAlex ID: W2803264515
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Wikidata QID: Q129891049
DOI: 10.1515/MSDS-2018-0006
description: scientific article; zbMATH DE number 6881274