Topological degree for (S)+-mappings with maximal monotone perturbations and its applications to variational inequalities

Jun Kobayashi; Mitsuharu Otani

doi:10.1016/j.na.2004.07.007

Topological degree for (S)+-mappings with maximal monotone perturbations and its applications to variational inequalities

Jun Kobayashi, Mitsuharu Otani^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

This paper is concerned with the topological degree for mappings of class (S)+ with maximal monotone perturbations.Several results and remarks concerning the evaluation of this degree are given. In particular, it is shown that the local degree for the generalized gradient of nonsmooth functional at the local minimizer is equal to one.As applications, two examples of elliptic variational inequalities are given, where the multiple existence of solutions is discussed.

Original language	English
Pages (from-to)	147-172
Number of pages	26
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	59
Issue number	1-2
DOIs	https://doi.org/10.1016/j.na.2004.07.007
Publication status	Published - 2004 Oct

Keywords

Elliptic variational inequality
Local minimizer of non-smooth functional
Mapping of class (S)+
Maximal monotone operator
Subdifferential operator
Topological degree

ASJC Scopus subject areas

Analysis
Applied Mathematics
Mathematics(all)

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10.1016/j.na.2004.07.007

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abstract = "This paper is concerned with the topological degree for mappings of class (S)+ with maximal monotone perturbations.Several results and remarks concerning the evaluation of this degree are given. In particular, it is shown that the local degree for the generalized gradient of nonsmooth functional at the local minimizer is equal to one.As applications, two examples of elliptic variational inequalities are given, where the multiple existence of solutions is discussed.",

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AB - This paper is concerned with the topological degree for mappings of class (S)+ with maximal monotone perturbations.Several results and remarks concerning the evaluation of this degree are given. In particular, it is shown that the local degree for the generalized gradient of nonsmooth functional at the local minimizer is equal to one.As applications, two examples of elliptic variational inequalities are given, where the multiple existence of solutions is discussed.

KW - Elliptic variational inequality

KW - Local minimizer of non-smooth functional

KW - Mapping of class (S)+

KW - Maximal monotone operator

KW - Subdifferential operator

KW - Topological degree

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Topological degree for (S)+-mappings with maximal monotone perturbations and its applications to variational inequalities

Abstract

Keywords

ASJC Scopus subject areas

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