Existence of Solutions for Nonlinear Implicit Differential Equations: An Equilibrium Problem Approach. (1st November 2016)

• Record Type: Journal Article
• Authors: Chadli, Ouayl; Ansari, Qamrul Hasan; Al-Homidan, Suliman
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 11(2016)
• Page Start: 1385
• Page End: 1419
• Publication Date: 2016-11-01
• Subjects: Evolution equations -- evolution triple -- maximal monotone operators -- mixed equilibrium problems -- nonmonotone perturbations -- pseudomonotone operators -- quasimonotone operators; 35J50 -- 35J60 -- 49J40 -- 49J15 -- 34A09; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1210164
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we study the existence of solutions for nonlinear implicit differential equations associated to a time-dependent pseudomonotone (respectively, quasimonotone) operator by using a new approach based on the theory of equilibrium \hboxproblems. More precisely, we first establish some existence results of solutions for mixed equilibrium problems where the \hboxbifunctions are, respectively, maximal monotone and \hboxpseudomonotone (quasimonotone) in the topological sense. Then, we write the nonlinear implicit differential equations in the form of a mixed equilibrium problem. By using the existence results for mixed equilibrium problems, we establish the existence of solutions of nonlinear implicit differential equations. This new approach provides some new and nice results which improve and unify most of the recent results obtained in this direction.