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Keywords:
existence of solutions; anti-periodic; monotone operator; maximal monotone operator; Schaefer fixed-point theorem; monotonicity method; diffusion equation
Summary:
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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