Existence of Solutions for Nonlinear Implicit Differential Equations: An Equilibrium Problem Approach |
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Authors: | Ouayl Chadli Suliman Al-Homidan |
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Institution: | 1. Department of Economics, Ibn Zohr University, Agadir, Morocco;2. Department of Mathematics and Statistics, King Fahd University of Petroleum &3. Minerals, Dhahran, Saudi Arabia |
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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. |
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Keywords: | Evolution equations evolution triple maximal monotone operators mixed equilibrium problems nonmonotone perturbations pseudomonotone operators quasimonotone operators |
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