Periodic solutions of superlinear autonomous Hamiltonian systems with prescribed period
type: Item
instance of: scholarly article
title: Periodic solutions of superlinear autonomous Hamiltonian systems with prescribed period
zbMATH Open document ID: 1104.37040
author: Tianqing An
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-12-07T00:00:00Z
review text: We prove an existence theorem for nonconstant periodic solutions of the superlinear autonomous Hamiltonian system \(\dot x(t)=J\nabla H(x(t))\) with prescribed period under an assumption weaker than the Ambrosetti-Rabinowitz-type condition \[ 0<\mu H(x)\leq (\nabla H(x),x\rangle,\quad \mu>2,\;|x|\geq R>0. \] Our result extends the pioneering work of \textit{P. H. Rabinowitz} [Commun. Pure Appl. Math. 31, 156--184 (1978; Zbl 0358.70014)]
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5077873
zbMATH Keywords: periodic solution
zbMATH Keywords: Ambrosetti-Rabinowitz-type condition
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: critical point
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.11.004
OpenAlex ID: W2012169965
cites work: Existence of multiple periodic orbits of Hamiltonian systems on positive-type hypersurfaces in \({\mathbb{R}}^{2n}\)
cites work: On the number of periodic orbits of Hamiltonian systems on positive-type hypersurfaces in \(\mathbb{R}^{2n}\)
cites work: Periodic orbits of Hamiltonian systems on symmetric positive-type hypersurfaces
cites work: Critical point theorems for indefinite functionals
cites work: Periodic solutions for a class of non-autonomous Hamiltonian systems
cites work: Periodic solutions of hamiltonian systems
cites work: Q3749777
DOI: 10.1016/J.JMAA.2005.11.004
Recommended article: Periodic solutions of superlinear convex autonomous Hamiltonian systems
Recommended article: Q3610645
Recommended article: Periodic solutions to superlinear planar Hamiltonian systems
Recommended article: Q3132431
Recommended article: Q3518095
Recommended article: Periodic solutions for a class of superquadratic Hamiltonian systems
Recommended article: Q5758509
Recommended article: Periodic solutions of asymptotically linear autonomous Hamiltonian systems
Recommended article: Periodic solutions for a class of autonomous Hamiltonian systems
Recommended article: Periodic solutions of ''superquadratic'' Hamiltonian systems
description: scientific article; zbMATH DE number 5077873