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On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space
- Source :
- Arab Journal of Mathematical Sciences. 29:29-51
- Publication Year :
- 2021
- Publisher :
- Emerald, 2021.
-
Abstract
- PurposeIn 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/approachAn approximation procedure and some priori estimates are used to solve the problem.FindingsThe 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/valueTo 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.
Details
- ISSN :
- 25889214 and 13195166
- Volume :
- 29
- Database :
- OpenAIRE
- Journal :
- Arab Journal of Mathematical Sciences
- Accession number :
- edsair.doi...........07e9b3989a3c7ff6e2bccb8b3f8ecab2