Existence of homoclinic orbits for Hamiltonian systems with superquadratic potentials
type: Item
instance of: scholarly article
title: Existence of homoclinic orbits for Hamiltonian systems with superquadratic potentials
zbMATH Open document ID: 1187.37086
DOI: 10.1155/2009/128624
author: Jian Ding
author: Junxiang Xu
author: Fubao Zhang
published in: Abstract and Applied Analysis
publication date: 2010-04-08T00:00:00Z
full work available at URL: https://eudml.org/doc/225941
review text: Summary: This paper concerns solutions for the Hamiltonian system: \(\dot z={\mathcal J}H_z(t,z)\). Here \(H(t,z)=(1/2)z\cdot Lz+ W(t,z)\), \(L\) is a \(2N\times 2N\) symmetric matrix, and \(W\in C^1(\mathbb R\times\mathbb R^{2N},\mathbb R)\). We consider the case that \(0\in\sigma_c(-({\mathcal J}(d/dt)+L))\) and \(W\) satisfies some superquadratic condition different from the type of Ambrosetti-Rabinowitz. We study this problem by virtue of some weak linking theorem recently developed and prove the existence of homoclinic orbits.
Mathematics Subject Classification ID: 37J45
zbMATH DE Number: 5690896
zbMATH Keywords: homoclinic orbits
zbMATH Keywords: superquadratic condition
zbMATH Keywords: Hamiltonian system
Wikidata QID: Q58646528
MaRDI profile type: Publication
OpenAlex ID: W2149754724
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description: scientific article; zbMATH DE number 5690896