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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Abstract

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 $L^{1}(\Omega)$.

Article information

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

Dates
First available in Project Euclid: 21 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1458588656

Digital Object Identifier
doi:10.12775/TMNA.2015.063

Mathematical Reviews number (MathSciNet)
MR3494963

Zentralblatt MATH identifier
1362.35130

Citation

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. https://projecteuclid.org/euclid.tmna/1458588656


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