Geodesic
Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions
Applications of Mathematics, Tome 63 (2018) no. 5, pp. 523-539
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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.
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.
DOI : 10.21136/AM.2018.0136-18
Classification : 35K10, 35K55, 35K57, 35K59, 35K90, 47J35
Keywords: existence of solutions; anti-periodic; monotone operator; maximal monotone operator; Schaefer fixed-point theorem; monotonicity method; diffusion equation 
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     title = {Existence of solutions for nonlinear nonmonotone evolution equations in {Banach} spaces with anti-periodic boundary conditions},
     journal = {Applications of Mathematics},
     pages = {523--539},
     year = {2018},
     volume = {63},
     number = {5},
     doi = {10.21136/AM.2018.0136-18},
     mrnumber = {3870147},
     zbl = {06986924},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0136-18/}
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Boussandel, Sahbi. Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions. Applications of Mathematics, Tome 63 (2018) no. 5, pp. 523-539. doi: 10.21136/AM.2018.0136-18

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