Existence of homoclinic solutions for the second-order discrete \(p\)-Laplacian systems
type: Item
instance of: scholarly article
title: Existence of homoclinic solutions for the second-order discrete \(p\)-Laplacian systems
zbMATH Open document ID: 1238.39002
author: Peng Chen
author: X. H. Tang
published in: Taiwanese Journal of Mathematics
publication date: 2011-12-19T00:00:00Z
review text: The authors study the following second-order discrete \(p\)-Laplacian system \[ \Delta (\varphi_p(\Delta u(n-1)))-a(n)|u(n)|^{p-2}u(n)+\nabla W(n,u(n))=0,\tag{\(*\)} \] where \(p>1\), \(\varphi_p(s)=|s|^{p-2}s\), \(n\in \mathbb{Z}\), \(u\in \mathbb{R}^N\), \(a:\mathbb{Z}\to \mathbb{R}\) and \(W: \mathbb{Z}\times \mathbb{R}^N\to\mathbb{R}\). System \((*)\) can be regarded as the discretization of a second order Hamiltonian system. The focus is on the existence of homoclinic orbits of \((*)\) emanating from \(0\) since homoclinic orbits play an important role in analyzing the chaos of dynamical systems. With the help of critical point theory, several sufficient conditions on the existence of at least one or infinitely many homoclinic orbits are established. The obtained results improve some existing ones.
reviewed by: Yuming Chen
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 5990176
zbMATH Keywords: second-order discrete \(p\)-Laplacian system
zbMATH Keywords: critical point theory
zbMATH Keywords: second order Hamiltonian system
zbMATH Keywords: homoclinic orbits
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500406426
OpenAlex ID: W4252105421
DOI: 10.11650/TWJM/1500406426
description: scientific article; zbMATH DE number 5990176