Periodic and homoclinic solutions of some semilinear sixth-order differential equations
type: Item
instance of: scholarly article
title: Periodic and homoclinic solutions of some semilinear sixth-order differential equations
zbMATH Open document ID: 1017.34046
DOI: 10.1016/S0022-247X(02)00153-1
author: Stepan Agop Tersian
author: J. V. Chaparova
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: The solvability of the boundary value problem \((P)\) \[ u^{vi}+Au^{iv}+Bu''+u-u^3=0, \quad 0<x<L, \] \[ u(0)=u''(0)=u^{iv}(0)=0, \quad u(L)=u''(L)=u^{iv}(L)=0, \] is considered, where \(A\) and \(B\) are positive constants such that \(A^{2}<4B\). The existence of a nontrivial solution follows by applying a minimization theorem and a multiplicity result based on Clark's theorem. The mountain-pass theorem of Brezis-Nirenberg and concentration-compactness arguments are used to establish the existence of homoclinic solutions to \[ u^{vi}+A^{iv}+Bu''-u+a(x)u|u|^{\sigma}=0, \] where \(a\) is positive periodic function and \(\sigma\) is a positive constant.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 1836786
zbMATH Keywords: periodic and homoclinic solutions
zbMATH Keywords: sixth-order equations
zbMATH Keywords: mountain-pass theorem
reviewed by: Klaudiusz Wójcik
MaRDI profile type: Publication
cites work: The Existence of Travelling Wave Solutions of a Generalized Phase-Field Model
cites work: Q4146134
cites work: Remarks on finding critical points
cites work: Periodic and homoclinic orbits for Lorentz-Lagranian systems via variational methods
cites work: Q5636090
cites work: A variational approach to homoclinic orbits in Hamiltonian systems
cites work: Critical point theory and Hamiltonian systems
cites work: Q4888372
cites work: Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations
cites work: Periodic and homoclinic solutions of extended Fisher-Kolmogorov equations
full work available at URL: s0022-247x(02)00153-1
OpenAlex ID: W1966694644
description: scientific article; zbMATH DE number 1836786