On the Bolza problem
type: Item
instance of: scholarly article
title: On the Bolza problem
zbMATH Open document ID: 0923.34025
author: Philippe Bolle
published in: Journal of Differential Equations
publication date: 1999-05-03T00:00:00Z
review text: A sufficient condition is obtained for the existence of infinitely many solutions to the problem \[ \ddot x+\nabla V(x)= 0,\quad x(0)= x_0,\quad x(T)= x_1, \] where \(T>0\), \(x_0,x_1\in \mathbb{R}^n\) are given. It is assumed that \(V\in C^2(\mathbb{R}^n,\mathbb{R})\) is even and for some \(p>2\) satisfies the inequality \(0<pV(x)\leq (\nabla V(x),x)\) for all large \(| x|\).
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1283664
zbMATH Keywords: solvability
zbMATH Keywords: Bolza problem
zbMATH Keywords: variational methods
zbMATH Keywords: infinitely many solutions
reviewed by: Sergei A. Brykalov
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3484
OpenAlex ID: W2136504495
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DOI: 10.1006/JDEQ.1998.3484
description: scientific article; zbMATH DE number 1283664