Minimax Theory and its Applications 09 (2024), No. 2, 185--200
Copyright Heldermann Verlag 2024
A Ky Fan Minimax Inequality Approach to Implicit Obstacle Problems of Fractional Laplacian Type Involving a Generalized Gradient Operator
Ouayl Chadli
(1) Department of Mathematics, University of Central Florida, Orlando, U.S.A.
(2) Ibn Zohr University, Agadir, Morocco
ochadli@gmail.com
Ram N. Mohapatra
Department of Mathematics, University of Central Florida, Orlando, U.S.A.
ram.mohapatra@ucf.edu
Abdellatif Koukkous
Department of Economics, Ibn Zohr University, Agadir, Morocco
a.koukkous@uiz.ac.ma
We study the existence of solutions of a constrained obstacle problem driven by a generalized fractional Laplace operator and involving Clarke's generalized gradient, where the constraint depends on the unknown state variable. We use a method based on the Ky Fan minimax inequality approach and recent developments in that theory. Our results are new and improve considerably recent results in literature.
Keywords: Hemivariational inequalities, pseudomonotone operators, equilibrium problems, maximal bifunctions, pseudomonotone bifunctions.
MSC: 49J40, 47J20, 90C33, 65K10, 49M20.
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