Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions

Applications of mathematics

Sahbi Boussandel^1¹ 

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

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

DOI  :  10.21136/AM.2018.0136-18

学科分类：应用数学

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown