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Topological Methods in Nonlinear Analysis

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

Authors

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

DOI:

https://doi.org/10.12775/TMNA.2015.063

Keywords

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

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

References

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Vol 46, No 2 (December 2015)

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Published

2015-12-01

How to Cite

1.
BENBOUBKER, Mohamed Badr, CHRAYTEH, Houssam, HJIAJ, Hassane and YAZOUGH, Chihab. Existence of solutions in the sense of distributions of anisotropic nonlinear elliptic equations with variable exponent. Topological Methods in Nonlinear Analysis. Online. 1 December 2015. Vol. 46, no. 2, pp. 665 - 694. [Accessed 1 July 2025]. DOI 10.12775/TMNA.2015.063.
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