Noncoercive mixed equilibrium problems under pseudomonotone perturbations and applications to nonlinear evolution equations with lack of coercivity

Suliman Al-Homidan; Qamrul Hasan Ansari; Ouayl Chadli

doi:10.1080/00036811.2017.1419198

Noncoercive mixed equilibrium problems under pseudomonotone perturbations and applications to nonlinear evolution equations with lack of coercivity

Suliman Al-Homidan, Qamrul Hasan Ansari^*, Ouayl Chadli

^*Corresponding author for this work

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

3 Scopus citations

Abstract

In this paper, we study the existence of solutions for noncoercive mixed equilibrium problems which are described by the sum of a maximal monotone bifunction and a pseudomonotone (or quasimonotone) bifunction in the sense of Brézis. Our approach is based on recession analysis and on recent results established by the authors for the existence of solutions of mixed equilibrium problems under pseudomonotone perturbations. As an application, we study the existence of solutions for nonlinear evolution equations associated with a noncoercive time-dependent pseudomonotone (or quasimonotone) operator.

Original language	English
Pages (from-to)	1199-1223
Number of pages	25
Journal	Applicable Analysis
Volume	98
Issue number	7
DOIs	https://doi.org/10.1080/00036811.2017.1419198
State	Published - 19 May 2019

Bibliographical note

Publisher Copyright:
© 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

34G20
47J30
49J40
49J53
Mixed equilibrium problems
evolution equations
maximal monotone operators/bifunctions
pseudomonotone operators/bifunctions in Brézis sense
quasimonotone operators/bifunctions in topological sense
recession analysis

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/00036811.2017.1419198

Cite this

@article{79113e07dc55471d90c398ecaddcd7d2,

title = "Noncoercive mixed equilibrium problems under pseudomonotone perturbations and applications to nonlinear evolution equations with lack of coercivity",

abstract = "In this paper, we study the existence of solutions for noncoercive mixed equilibrium problems which are described by the sum of a maximal monotone bifunction and a pseudomonotone (or quasimonotone) bifunction in the sense of Br{\'e}zis. Our approach is based on recession analysis and on recent results established by the authors for the existence of solutions of mixed equilibrium problems under pseudomonotone perturbations. As an application, we study the existence of solutions for nonlinear evolution equations associated with a noncoercive time-dependent pseudomonotone (or quasimonotone) operator.",

keywords = "34G20, 47J30, 49J40, 49J53, Mixed equilibrium problems, evolution equations, maximal monotone operators/bifunctions, pseudomonotone operators/bifunctions in Br{\'e}zis sense, quasimonotone operators/bifunctions in topological sense, recession analysis",

author = "Suliman Al-Homidan and Ansari, \{Qamrul Hasan\} and Ouayl Chadli",

note = "Publisher Copyright: {\textcopyright} 2017, {\textcopyright} 2017 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2019",

month = may,

day = "19",

doi = "10.1080/00036811.2017.1419198",

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T1 - Noncoercive mixed equilibrium problems under pseudomonotone perturbations and applications to nonlinear evolution equations with lack of coercivity

AU - Al-Homidan, Suliman

AU - Ansari, Qamrul Hasan

AU - Chadli, Ouayl

PY - 2019/5/19

Y1 - 2019/5/19

N2 - In this paper, we study the existence of solutions for noncoercive mixed equilibrium problems which are described by the sum of a maximal monotone bifunction and a pseudomonotone (or quasimonotone) bifunction in the sense of Brézis. Our approach is based on recession analysis and on recent results established by the authors for the existence of solutions of mixed equilibrium problems under pseudomonotone perturbations. As an application, we study the existence of solutions for nonlinear evolution equations associated with a noncoercive time-dependent pseudomonotone (or quasimonotone) operator.

AB - In this paper, we study the existence of solutions for noncoercive mixed equilibrium problems which are described by the sum of a maximal monotone bifunction and a pseudomonotone (or quasimonotone) bifunction in the sense of Brézis. Our approach is based on recession analysis and on recent results established by the authors for the existence of solutions of mixed equilibrium problems under pseudomonotone perturbations. As an application, we study the existence of solutions for nonlinear evolution equations associated with a noncoercive time-dependent pseudomonotone (or quasimonotone) operator.

KW - 34G20

KW - 47J30

KW - 49J40

KW - 49J53

KW - Mixed equilibrium problems

KW - evolution equations

KW - maximal monotone operators/bifunctions

KW - pseudomonotone operators/bifunctions in Brézis sense

KW - quasimonotone operators/bifunctions in topological sense

KW - recession analysis

UR - https://www.scopus.com/pages/publications/85039754258

U2 - 10.1080/00036811.2017.1419198

DO - 10.1080/00036811.2017.1419198

M3 - Article

AN - SCOPUS:85039754258

SN - 0003-6811

VL - 98

SP - 1199

EP - 1223

JO - Applicable Analysis

JF - Applicable Analysis

IS - 7

ER -

Noncoercive mixed equilibrium problems under pseudomonotone perturbations and applications to nonlinear evolution equations with lack of coercivity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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