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Existence of Solutions for Nonlinear Nonmonotone Evolution Equations in Banach Spaces with Anti-Periodic Boundary Conditions

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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.

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Authors and Affiliations

  1. Faculty of Sciences of Bizerte, Department of Mathematics, 7021 Jarzouna Bizerte, University of Carthage, Laboratoire EDP et Applications, LR03ES04, Bizerte, Tunisia

    Sahbi Boussandel

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  1. Sahbi Boussandel
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Boussandel, S. Existence of Solutions for Nonlinear Nonmonotone Evolution Equations in Banach Spaces with Anti-Periodic Boundary Conditions. Appl Math 63, 523–539 (2018). https://doi.org/10.21136/AM.2018.0136-18

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