Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations

Ouayl Chadli (), Qamrul Hasan Ansari () and Jen-Chih Yao ()
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Ouayl Chadli: Ibn Zohr University
Qamrul Hasan Ansari: Aligarh Muslim University
Jen-Chih Yao: China Medical University

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 2, No 2, 410-440

Abstract: Abstract By using some new developments in the theory of equilibrium problems, we study the existence of anti-periodic solutions for nonlinear evolution equations associated with time-dependent pseudomonotone and quasimonotone operators in the topological sense. More precisely, we establish new existence results for mixed equilibrium problems associated with pseudomonotone and quasimonotone bifunctions in the topological sense. The results obtained are therefore applied to study the existence of anti-periodic solutions for nonlinear evolution equations in the setting of reflexive Banach spaces. This new approach leads us to improve and unify most of the recent results obtained in this direction.

Keywords: Mixed equilibrium problems; Evolution equations; Anti-periodic solutions; Maximal monotone operators; Pseudomonotone operators; Quasimonotone operators; Nonmonotone perturbations; 49J40; 49K40; 90C31; 34B10; 24B15 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-015-0707-y

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