Existence of multiple critical points for an asymptotically quadratic functional with applications
type: Item
instance of: scholarly article
title: Existence of multiple critical points for an asymptotically quadratic functional with applications
zbMATH Open document ID: 0938.58013
DOI: 10.1155/S1085337596000140
author: Jiabao Su
author: Shujie Li
published in: Abstract and Applied Analysis
publication date: 2000-06-14T00:00:00Z
full work available at URL: https://eudml.org/doc/48438
full work available at URL: issue-3.html
review text: Let \(X\) be a Hilbert space and let \(f\in{\mathcal C}^1(X)\) be an asymptotically quadratic functional with resonance at infinity, so \(f'(x)=Ax+o(|x|)\) as \(|x|\to\infty\) and the selfadjoint operator \(A\in{\mathcal{L}}(X)\) has a kernel. The abstract results of the paper yield the existence of one or two critical points provided a certain angle condition at infinity holds (plus some standard conditions). The proof depends on computations of the critical groups at infinity and at isolated, possibly degenerate critical points. The results are applied to the existence of periodic solutions of asymptotically linear second order Hamiltonian systems with resonance at infinity. The main new contributions are conditions on the Hamiltonian which imply the angle condition for the associated functional.
reviewed by: Thomas J. Bartsch
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1370660
zbMATH Keywords: Morse theory
zbMATH Keywords: degenerate critical points
zbMATH Keywords: periodic solutions of Hamiltonian systems
zbMATH Keywords: resonance at infinity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1370660