A non-smooth two points boundary value problem on Riemannian manifolds
type: Item
instance of: scholarly article
title: A non-smooth two points boundary value problem on Riemannian manifolds
zbMATH Open document ID: 0833.58038
DOI: 10.1007/BF01765637
author: Elvira Mirenghi
author: Addolorata Salvatore
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1996-03-20T00:00:00Z
review text: The problem considered is to find solutions to the differential inclusion problem: \[ D_t x(t)\in \partial V(x(t))\;(\text{generalized gradient}) \] with boundary conditions \(x(0)= x_0\), \(x(1)= x_1\), on a Riemannian manifold. Here \(V\) is a locally Lipschitz continuous potential function. By an argument using the Lyusternik-Shnirelman critical point theory it is proven that, unless the manifold is contractible in itself, there are infinitely many solutions to this problem.
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 711481
zbMATH Keywords: differential inclusion problem
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: Lyusternik- Shnirelman critical point theory
Wikidata QID: Q115393191
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01765637
OpenAlex ID: W2069838488
description: scientific article; zbMATH DE number 711481