Multiplicity of Solutions for Fractional-Order Differential Equations via the κ(x)-Laplacian Operator and the Genus Theory

被引：31

作者：

Srivastava, Hari M. ^{[1
,2
,3
,4
]}

da Costa Sousa, Jose Vanterler ^{[5
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[3] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, AZ-1007 Baku, Azerbaijan

[4] Int Telemat Univ Uninettuno, Sect Math, I-00186 Rome, Italy

[5] Fed Univ ABC UFABC, Ctr Math Comp & Cognit, 5001 Bangu, BR-09210580 Santo Andre, SP, Brazil

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 09期

关键词：

fractional differential equations; kappa(x)-Laplacian; chi-Hilfer fractional derivative; existence; multiplicity of solutions; genus theory; Concentration-Compactness Principle; Mountain Pass Theorem; variable exponents; variational methods; P(X)-LAPLACIAN EQUATIONS; CRITICAL GROWTH; EXISTENCE; CALCULUS; FUNCTIONALS; SPACES;

D O I：

10.3390/fractalfract6090481

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the existence and multiplicity of solutions for a class of quasi-linear problems involving fractional differential equations in the chi-fractional space H-kappa(x)(gamma,beta,chi)(Delta). Using the Genus Theory, the Concentration-Compactness Principle, and the Mountain Pass Theorem, we show that under certain suitable assumptions the considered problem has at least k pairs of non-trivial solutions.

引用

页数：27

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