Variational and non-variational methods in nonlinear analysis and boundary value problems
type: Item
instance of: scholarly article
title: Variational and non-variational methods in nonlinear analysis and boundary value problems
zbMATH Open document ID: 1040.49001
published in: Nonconvex Optimization and Its Applications
publication date: 2003-09-21T00:00:00Z
review text: The book presents some modern topics in nonlinear analysis such as multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities, evolution problems and applications of these theories to some classes of boundary value problems. The treatment relies on variational methods, monotonicity principles, topological arguments and optimization techniques. More precisely, the authors deal with the following topics: -- nonsmooth critical point theories due to Clarke and Degiovanni, Goeleven-Motreanu-Panagiotopoulos, Szulkin; -- abstract multiplicity theorem of Lusternik-Schnirelman type and a Schrödinger type equation with lack of compactness; -- extremal solutions for initial boundary value problems of parabolic type involving Clarke's gradient; -- boundary value problems expressed by variational, hemivariational and variational-hemivariational inequalities; -- eigenvalue problems with symmetries; -- non-symmetric perturbations of symmetric eigenvalue problems; -- the location of critical points for nonsmooth functionals; -- first order evolution quasivariational inequalities and second order nonlinear evolution equations; -- stability results regarding variational inequalities; -- variational approach involving a functional not satisfying the Palais-Smale condition.
Mathematics Subject Classification ID: 49-02
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1983463
zbMATH Keywords: variational methods
zbMATH Keywords: boundary value problems
zbMATH Keywords: critical point theory
zbMATH Keywords: hemivariational inequalities
zbMATH Keywords: eigenvalue problems
author: Dumitru Motreanu
author: Vicenţiu D. Rădulescu
reviewed by: Leszek Gasiński
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1983463