Global existence and boundedness for quasi-variational systems
type: Item
instance of: scholarly article
title: Global existence and boundedness for quasi-variational systems
zbMATH Open document ID: 0942.34006
DOI: 10.1155/S0161171299222818
author: Giancarlo Cantarelli
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1999-11-23T00:00:00Z
full work available at URL: https://eudml.org/doc/48490
review text: The author studies the quasi-variational ordinary differential system \[ \frac{d}{dt}(\nabla_p G(u,\dot{u}))-\nabla_u G(u,\dot{u}) +\nabla_u F(t,u)=Q(t,u,\dot{u}), \] where \(G(u,p)\) is a function of class \(C^1\), strictly convex in the variable \(p \in \mathbb{R}^N\) for every \(u \in {\mathbb R}^N\), with \(G(u,0)=0\) and \(\nabla G(u,0)=0\) on \(\mathbb{R}^N.\) This system may be considered as the motion law for holonomic mechanical systems. Sufficient conditions for the global existence of solutions to system (1) in the future and for their partial boundedness are obtained by constructing appropriate Lyapunov functions and using the comparison method.
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 1334834
zbMATH Keywords: quasi-variational ordinary differential systems
zbMATH Keywords: global existence in the future
zbMATH Keywords: partial boundedness
zbMATH Keywords: Lyapunov function
zbMATH Keywords: comparison method
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1334834