On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Emerald Publishing
2023-01-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-12-2020-0133/full/pdf |
| Summary: | 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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| ISSN: | 1319-5166 2588-9214 |