Arab Journal of Mathematical Sciences (Jan 2023)

On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space

  • Omar Benslimane,
  • Ahmed Aberqi,
  • Jaouad Bennouna

DOI
https://doi.org/10.1108/AJMS-12-2020-0133
Journal volume & issue
Vol. 29, no. 1
pp. 29 – 51

Abstract

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Purpose – In the present paper, the authors will discuss the solvability of a class of nonlinear anisotropic elliptic problems (P), with the presence of a lower-order term and a non-polynomial growth which does not satisfy any sign condition which is described by an N-uplet of N-functions satisfying the Δ2-condition, within the fulfilling of anisotropic Sobolev-Orlicz space. In addition, the resulting analysis requires the development of some new aspects of the theory in this field. The source term is merely integrable. Design/methodology/approach – An approximation procedure and some priori estimates are used to solve the problem. Findings – The authors prove the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain. The resulting analysis requires the development of some new aspects of the theory in this field. Originality/value – To the best of the authors’ knowledge, this is the first paper that investigates the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain.

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