Periodic solutions for a class of symmetric and subquadratic Hamiltonian systems
type: Item
instance of: scholarly article
title: Periodic solutions for a class of symmetric and subquadratic Hamiltonian systems
zbMATH Open document ID: 0862.34036
DOI: 10.1016/0895-7177(96)00029-5
author: Yanheng Ding
author: Mario Girardi
published in: Mathematical and Computer Modelling
publication date: 1997-05-26T00:00:00Z
review text: The authors consider a Hamiltonian system \(\dot z= JH_z(t,z)\), where \(H\in C^1 (\mathbb{R} \times \mathbb{R}^{2N}, \mathbb{R})\) is \(T\)-periodic in \(t\), even in \(z\) and subquadratic at \(z=0\). It is shown that under some additional hypotheses this system has infinitely many \(T\)-periodic solutions \(z_m\) which tend to zero as \(m\to\infty\). If moreover \(H\) is of the form \(H(t, z) = B(t)W(z)\) and \(T\) is the minimal period of \(B\), then \(T\) is also the minimal period of \(z_m\) for each \(m\). The proof uses a minimax argument and Krasnosel'skij's genus together with a Galerkin-type procedure (which is needed because the functional associated with the problem is strongly indefinite).
reviewed by: Andrzej Szulkin
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 915017
zbMATH Keywords: minimax method
zbMATH Keywords: periodic solutions
zbMATH Keywords: Hamiltonian
zbMATH Keywords: genus
MaRDI profile type: Publication
full work available at URL: 0895-7177(96)00029-5
OpenAlex ID: W2018208627
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description: scientific article; zbMATH DE number 915017