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

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

DOI: http://dx.doi.org/10.12775/TMNA.2015.063


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


Anisotropic Sobolev spaces; variable exponent; strongly nonlinear elliptic equations; boundary value problems; solution in the sense of distributions

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