Existence and multiplicity of solutions for some Styklov problem involving <i>p</i>(<i>x</i>)-Laplacian operator

Chammem, R.; Ghanmi, Abdeljabbar; Sahbani, A.

doi:10.1080/00036811.2020.1807014

Cited by 15 publications

(3 citation statements)

References 18 publications

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“…In [4], Bahrouni and Radulescu obtained some further qualitative properties of these new spaces. After that, some studies on this context have been performed by using different approaches, see [3,5,6,13,14,15,26]. In these last references, the authors established a compact embedding theorems and proved some further qualitative properties of the fractional Sobolev space with variable exponent and the fractional p(x, •)−Laplace operator.…”

Section: Introductionmentioning

confidence: 99%

Comparison and sub-supersolution principles for the fractional p(x)-Laplacian

Bahrouni

2018

Journal of Mathematical Analysis and Applications

100

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Section: Introductionmentioning

confidence: 99%

Comparison and sub-supersolution principles for the fractional p(x)-Laplacian

Bahrouni

2018

Journal of Mathematical Analysis and Applications

100

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“…In this section, we recall some necessary properties of variable exponent spaces. We refer the reader to [1,2,4,5,6,7,8,26].…”

Section: Preliminariesmentioning

confidence: 99%

Multiplicity of solutions for variable-order fractional Kirchhoff problem with singular term

Chammem,

Sahbani,

Saidani

2024

Quaestiones Mathematicae

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In this paper, we consider a class of singular variable-order fractional Kirchhoff problem of the form:where .) is the variable-order fractional Laplacian operator, [u] s(.) is the Gagliardo seminorm and s(.) : R N × R N → (0, 1) is a continuous and symetric function. We assume that λ is a non-negative parameter , σ ≥ 1, m, q ∈ C(Ω) with 0 < m(x) < 1 < 2σ < q(x) < 2 * s(.) for all x ∈ Ω. We combine some variational techniques with a truncation argument in order to show the existence and the multiplicity of positive solutions for the above problem.

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“…In addition, problems of type (1.1), can describe the static from change of beam or the sport of rigid body. Due to their importance, many researchers focused on the study of such problems see for example [1,7,14] and references therein. The interplay between the fourth-order equation and the variable exponent equation goes to the p(x)-biharmonic problems.…”

mentioning

confidence: 99%

Multiplicity of Solutions for Some $p(x)$-Biharmonic Problem

Ghanmi¹

2021

Bulletin of the Inst. of Math. Academia Sinica(N.S.)

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This paper deals with the study of some class of non-homogeneous problems involving the p(x)-biharmonic operator. Using direct variational methods, the existence of nontrivial solution is obtained. The multiplicity of solutions is obtained by combining Ekeland's variational principle with the Mountain pass theorem. Finally, the Fountain theorem is applied to prove the existence of infinetely many solutions for the given problem.

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Existence and multiplicity of solutions for some Styklov problem involving p(x)-Laplacian operator

Cited by 15 publications

References 18 publications

Comparison and sub-supersolution principles for the fractional p(x)-Laplacian

Comparison and sub-supersolution principles for the fractional p(x)-Laplacian

Multiplicity of solutions for variable-order fractional Kirchhoff problem with singular term

Multiplicity of Solutions for Some $p(x)$-Biharmonic Problem

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