Topological Methods in Nonlinear Analysis

Existence of solutions in the sense of distributions of anisotropic nonlinear elliptic equations with variable exponent

Mohamed Badr Benboubker, Houssam Chrayteh, Hassane Hjiaj, and Chihab Yazough

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The aim of this paper is to study the existence of solutions in the sense of distributions for a strongly nonlinear elliptic problem where the second term of the equation $f$ is in $ W^{-1,\overrightarrow{p}'(\,\cdot\,)}(\Omega)$ which is the dual space of the anisotropic Sobolev $W_{0}^{1,\overrightarrow{p}(\,\cdot\,)}(\Omega)$ and later $f$ will be in $L^{1}(\Omega)$.

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Topol. Methods Nonlinear Anal., Volume 46, Number 2 (2015), 665-693.

First available in Project Euclid: 21 March 2016

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Benboubker, Mohamed Badr; Chrayteh, Houssam; Hjiaj, Hassane; Yazough, Chihab. Existence of solutions in the sense of distributions of anisotropic nonlinear elliptic equations with variable exponent. Topol. Methods Nonlinear Anal. 46 (2015), no. 2, 665--693. doi:10.12775/TMNA.2015.063.

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