Superlinear variational and boundary value problems with parameters
type: Item
instance of: scholarly article
title: Superlinear variational and boundary value problems with parameters
zbMATH Open document ID: 0982.49003
DOI: 10.1016/S0362-546X(99)00189-3
author: Stanislaw Walczak
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-04-11T00:00:00Z
review text: The paper is devoted to the question of the continuous dependence on parameters \(w\) of the set of critical points of the functional \[ F_w(u)= \int_\Omega \Biggl[{1\over 2}|\nabla u(x)|^2- G(x,u(x), w(x))\Biggr] dx \] defined on \(H^1_0(\Omega)\) and the set of solutions of the associated Euler-Lagrange system \[ \Delta u(x)+ \nabla_u G(x,u(x), w(x)) \] under the assumption of superlinearity \[ a< pG(x,u,w)\leq \langle\nabla_u G(x,u,w), u\rangle \] for some \(a> 0\) and \(p> 2\). Some special attention is paid to the one-dimensional problem.
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 1545350
zbMATH Keywords: superlinear problem
zbMATH Keywords: well-posedness
zbMATH Keywords: critical points
reviewed by: Jean Mawhin
MaRDI profile type: Publication
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full work available at URL: s0362-546x(99)00189-3
OpenAlex ID: W2008430636
Wikidata QID: Q127610255
description: scientific article; zbMATH DE number 1545350