Existence and uniqueness of entropy solution of a nonlinear elliptic equation in anisotropic Sobolev–Orlicz space

Benslimane, Omar; Aberqi, Ahmed; Bennouna, Jaouad

doi:10.1007/s12215-020-00577-4

Cited by 16 publications

(15 citation statements)

References 32 publications

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“…If λ → 0 + due to q + < p + < r − , then ||u|| −→ +∞. Which contradicts (7). Lemma 4 Under assumptions (i)-(v), there exists λ * ∈ (0, λ * ] such that N ± λ = ∅ for all λ ∈ (0, λ * ).…”

Section: Thusmentioning

confidence: 92%

“…In particular, using the theory of pseudomonotone operators, Gasiński, and Winkert in [16] proved the existence and uniqueness of a weak solution to quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient, under quite general assumptions on the convection term and towering some linear conditions on the gradient variable. Finally, for a deeper comprehension, we refer the reader to [1,3,[5][6][7][8][9]11] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Existence of solutions for a singular double phase in Sobolev-Orlicz spaces with variable exponents in a complete manifold

Aberqi¹,

Bennouna²,

Benslimane³

et al. 2022

Preprint

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The purpose of this paper is to study a class of double phase problems, with a singular term and a superlinear parametric term on the right-hand side. Using the method of Nehari manifold combined with the fibering maps, we prove that for all small values of the parameter λ > 0, there exist at least two non-trivial positive solutions. Our results extend the previous works Papageorgiou, Repovš, and Vetro [24] and Liu, Dai, Papageorgiou, and Winkert [21], from the case of Musielak-Orlicz Sobolev space, when exponents p and q are constant, to the case of Sobolev-Orlicz spaces with variable exponents in a complete manifold.

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Section: Thusmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Existence of solutions for a singular double phase in Sobolev-Orlicz spaces with variable exponents in a complete manifold

Aberqi¹,

Bennouna²,

Benslimane³

et al. 2022

Preprint

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“…We will mention recent papers, and we are starting by the pertinent works of Korolev and Cianchi [25,26] who proved the embeddings of this space. Then, Benslimane, Aberqi and Bennouna in [27] studied the existence and uniqueness of the solution in the following problem in an unbounded domain ðPÞ…”

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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“…Also, there are many articles on nonstandard growth problems, especially on p(x)-growth and double phase problems. About p(x)-growth problems, see [1,2,4,5,6,7,8,9,11,12,22] and the references given there.…”

Section: Introductionmentioning

confidence: 99%

Existence Results for double phase problem in Sobolev-Orlicz spaces with variable exponents in Complete Manifold

Aberqi¹,

Bennouna²,

Benslimane³

et al. 2021

Preprint

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In this paper, we study the existence of non-negative non-trivial solutions for a class of double-phase problems where the source term is a Caratheodory function that satisfies the Ambrosetti-Rabinowitz type condition in the framework of Sobolev-Orlicz spaces with variable exponents in complete compact Riemannian n-manifolds. Our approach is based on the Nehari manifold and some variational techniques. Further-more, the Hölder inequality, continuous and compact embedding results are proved.

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Existence and uniqueness of entropy solution of a nonlinear elliptic equation in anisotropic Sobolev–Orlicz space

Cited by 16 publications

References 32 publications

Existence of solutions for a singular double phase in Sobolev-Orlicz spaces with variable exponents in a complete manifold

Existence of solutions for a singular double phase in Sobolev-Orlicz spaces with variable exponents in a complete manifold

On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space

Existence Results for double phase problem in Sobolev-Orlicz spaces with variable exponents in Complete Manifold

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