Multiple solutions of Hamiltonian systems via limit relative category
type: Item
instance of: scholarly article
title: Multiple solutions of Hamiltonian systems via limit relative category
zbMATH Open document ID: 0817.58007
DOI: 10.1016/0377-0427(94)90364-6
published in: Journal of Computational and Applied Mathematics
publication date: 1995-07-31T00:00:00Z
review text: Let \(E\) be a Hilbert space, \(V\) a manifold of class \(C^ 2\) and \(f \in C^ 1(E \times V, \mathbb{R})\) a strongly indefinite functional. In [\textit{G. Fourier, D. Lupo, M. Ramos} and \textit{M. Willem}, [Dynamics reported. Expositions in dynamical systems. New series Vol. 3, 1-24 (1994; Zbl 0794.58007)] it has been shown that if \(f\) satisfies a compactness condition of Palais-Smale type and a certain linking condition, then \(f\) possesses at least \(1 + \text{cuplength}(V)\) critical points. The main result of this paper asserts that the number of critical points is at least \(2+2 \text{cuplength}(V)\) provided a stronger linking condition is satisfied (roughly speaking, there are two subsets of \(E\), say \(A\) and \(B\), such that \(A\) is linked to \(B\), \(B\) is linked to \(A\) and the corresponding minimax levels are distinct). The paper ends in an application of the above result to asymptotically linear Hamiltonian system with periodic nonlinearity and to a superquadratic Hamiltonian system.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 711774
zbMATH Keywords: limit relative category
zbMATH Keywords: strongly indefinite functional
zbMATH Keywords: linking
zbMATH Keywords: Hamiltonian system
author: Daniela Lupo
author: Anna Maria Micheletti
reviewed by: Andrzej Szulkin
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90364-6
OpenAlex ID: W2092790389
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description: scientific article; zbMATH DE number 711774