Nonlinear p(x)-Elliptic Equations in General Domains

Azroul, Elhoussine; Khouakhi, Moussa; Yazough, Chihab

doi:10.1007/s12591-018-0433-7

Cited by 2 publications

(1 citation statement)

References 16 publications

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“…B enilan in [2] presented the idea of entropy solutions which were adjusted to the Boltzmann condition. For a deeper comprehension of these types of equations in this field, we refer the reader to [3][4][5][6][7][8][9][10] and references therein.…”

Section: Introductionmentioning

confidence: 99%

On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space

Benslimane

Aberqi

Bennouna

2021

AJMS

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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.

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