Three solutions for a nonlocal fractional<i>p</i>-Kirchhoff type elliptic system

Azroul, Elhoussine; Benkirane, Abdelmoujib; Boumazourh, Athmane; Srati, Mohammed

doi:10.1080/00036811.2019.1670347

Cited by 22 publications

(12 citation statements)

References 19 publications

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“…Of course, when pðxÞ ≡ pðorp = 2Þ and sð•Þ ≡ s, the operators in (1) reduce to the classical non-local fractional p -Laplacian, i.e., ð−ΔÞ s p (ð−ΔÞ s ). Similarly, for the Kirchhofftype system cases, the papers [14][15][16][17][18][19][20] introduce a lot of related work in recent years, where many authors studied the existence and multiplicity of solutions by applying variational methods. For instance, based on the three critical points theorem, Azroul et al ( [15]) discussed an elliptic system with the homogeneous Dirichlet boundary conditions, and they obtained the existence of three weak solutions.…”

Section: Introductionmentioning

confidence: 99%

A Class of Variable-Order Fractional $p (\cdot)$ -Kirchhoff-Type Systems

Wu¹,

Qiao

Hamdani

et al. 2021

Journal of Function Spaces

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This paper is concerned with an elliptic system of Kirchhoff type, driven by the variable-order fractional p x -operator. With the help of the direct variational method and Ekeland variational principle, we show the existence of a weak solution. This is our first attempt to study this kind of system, in the case of variable-order fractional variable exponents. Our main theorem extends in several directions previous results.

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Section: Introductionmentioning

confidence: 99%

A Class of Variable-Order Fractional $p (\cdot)$ -Kirchhoff-Type Systems

Wu¹,

Qiao

Hamdani

et al. 2021

Journal of Function Spaces

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“…For the problems involving fractional Kirchhoff type, we refer the reader to the works [1,[3][4][5][6], where the authors use different methods to establish the existence of solutions.…”

Section: Introductionmentioning

confidence: 99%

Existence of Solutions for a Class of Fractional Kirchhoff-type Systems in $\mathbb{R}^N$ with Non-standard Growth

2021

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This paper is concerned with the existence and multiplicity of nontrivial solutions for a class of Kirchhoff-type systems in R N involving the fractional pseudodifferential operators defined as the generalizations of the p(x)-Laplace operator. Our main tools come from a direct variational methods, the Mountain Pass Theorem, the symmetric Mountain Pass Theorem and the Fountain Theorem in critical point theory.The obtained results of this note significantly contribute to the study of Kirchhofftype systems in the sense that our situation covers not only differential operators of fractional order but also nonhomogeneous differential operators in Sobolev spaces with variable exponent.

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“…Motivated by [7,9,10,21], our main goal is to prove the existence of three positive solutions for problem (P 1 ). Our approach is based on the three critical points theorem introduced by Ricceri.…”

Section: Introductionmentioning

confidence: 99%

Three solutions for a fractional (p(x,.),q(x,.))-Kirchhoff type elliptic system

2020

J. Nonlinear Funct. Anal.

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Three solutions for a nonlocal fractionalp-Kirchhoff type elliptic system

Cited by 22 publications

References 19 publications

A Class of Variable-Order Fractional $p (\cdot)$ -Kirchhoff-Type Systems

A Class of Variable-Order Fractional $p (\cdot)$ -Kirchhoff-Type Systems

Existence of Solutions for a Class of Fractional Kirchhoff-type Systems in $\mathbb{R}^N$ with Non-standard Growth

Three solutions for a fractional (p(x,.),q(x,.))-Kirchhoff type elliptic system

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Three solutions for a nonlocal fractionalp-Kirchhoff type elliptic system

Cited by 22 publications

References 19 publications

A Class of Variable-Order Fractional p · -Kirchhoff-Type Systems

A Class of Variable-Order Fractional p · -Kirchhoff-Type Systems

Existence of Solutions for a Class of Fractional Kirchhoff-type Systems in $\mathbb{R}^N$ with Non-standard Growth

Three solutions for a fractional (p(x,.),q(x,.))-Kirchhoff type elliptic system

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A Class of Variable-Order Fractional $p (\cdot)$ -Kirchhoff-Type Systems

A Class of Variable-Order Fractional $p (\cdot)$ -Kirchhoff-Type Systems