Applications of Mathematics, Vol. 63, No. 5, pp. 523-539, 2018
Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions
Sahbi Boussandel
Received April 29, 2018. Published online October 5, 2018.
Abstract: The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet $p$-Laplace operator.
Keywords: existence of solutions; anti-periodic; monotone operator; maximal monotone operator; Schaefer fixed-point theorem; monotonicity method; diffusion equation
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Affiliations: Sahbi Boussandel, Faculty of Sciences of Bizerte, Department of Mathematics, 7021 Jarzouna Bizerte, University of Carthage, Laboratoire EDP et Applications LR03ES04, Bizerte, Tunisia, e-mail: sboussandels@gmail.com
