Periodic solutions with prescribed energy on non-complete Riemannian manifolds
type: Item
instance of: scholarly article
title: Periodic solutions with prescribed energy on non-complete Riemannian manifolds
zbMATH Open document ID: 0853.58085
author: Elvira Mirenghi
author: Maria Tucci
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-01-13T00:00:00Z
review text: The problem treated in this paper is to look for periodic solutions of the system \(D_t \dot x(t) = -\nabla V(x(t))\) that is defined on a Riemannian manifold for a \(C^1\) potential \(V\). The author considers the case where the Riemannian structure is not necessarily complete; instead, the author assumes the convexity of the boundary. The convexity is defined by an exhausting function whose gradient norm is finite and whose Hessian matrix is nonnegative. Then, by assuming that the fundamental group is finite or has infinite conjugacy classes, and with several additional conditions on the potential and convexity, the author shows the existence of non-trivial periodic solutions with energy estimate.
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 902562
zbMATH Keywords: convex boundary
zbMATH Keywords: periodic solutions
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0145
OpenAlex ID: W2077505949
Wikidata QID: Q115395419
DOI: 10.1006/JMAA.1996.0145
description: scientific article; zbMATH DE number 902562