INFINITELY MANY SOLUTIONS FOR FRACTIONAL SCHRODINGER-MAXWELL EQUATIONS

被引：17

作者：

Xu, Jiafa ^{[1
]}

Wei, Zhongli ^{[2
]}

O'Regan, Donal ^{[3
]}

Cui, Yujun ^{[4
]}

机构：

[1] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China

[2] Shandong Jianzhu Univ, Dept Math, Jinan 250101, Shandong, Peoples R China

[3] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

[4] Shandong Univ Sci & Technol, State Key Lab Min Disaster Prevent & Control Cofo, Qingdao 266590, Shandong, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2019年 / 9卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Fractional Laplacian; Schrodinger-Maxwell equations; infinitely many solutions; BOUNDARY-VALUE-PROBLEMS; KLEIN-GORDON-MAXWELL; BLOW-UP SOLUTIONS; NONTRIVIAL SOLUTIONS; POSITIVE SOLUTIONS; KIRCHHOFF TYPE; EXISTENCE; UNIQUENESS; SYSTEM;

D O I：

10.11948/2156-907X.20190022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper using fountain theorems we study the existence of infinitely many solutions for fractional Schrodinger-Maxwell equations {(-Delta)(alpha)u + lambda V(x)u + phi u = f(x,u) - mu g(x)vertical bar u vertical bar(q-2)u, in R-3, (-Delta)(alpha)phi = K(alpha)u(2), in R-3, where lambda, mu > 0 are two parameters, alpha is an element of (0,1], K-alpha = pi(-alpha)Gamma(alpha)/pi(-(3-2 alpha)/2)Gamma((3-2 alpha)/2) and (-Delta)(alpha) is the fractional Laplacian. Under appropriate assumptions on f and g we obtain an existence theorem for this system.

引用

页码：1165 / 1182

页数：18

共 52 条

[1] A THEORETICAL BASIS FOR THE APPLICATION OF FRACTIONAL CALCULUS TO VISCOELASTICITY [J].

BAGLEY, RL ;

TORVIK, PJ .

JOURNAL OF RHEOLOGY, 1983, 27 (03) :201-210

[2] On the existence of blow up solutions for a class of fractional differential equations [J].

Bai, Zhanbing ;

Chen, YangQuan ;

Lian, Hairong ;

Sun, Sujing .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2014, 17 (04) :1175-1187

[3] Solvability of fractional three-point boundary value problems with nonlinear growth [J].

Bai, Zhanbing ;

Zhang, Yinghan .

APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (05) :1719-1725

[4]

Benci V., 1998, Topol. Methods Nonlinear Anal., V11, P283, DOI DOI 10.12775/TMNA.1998.019

[5] Ground state solutions of asymptotically linear fractional Schrodinger equations [J].

Chang, Xiaojun .

JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (06)

[6] New Existence of Solutions for the Fractional p-Laplacian Equations with Sign-Changing Potential and Nonlinearity [J].

Cheng, Bitao ;

Tang, Xianhua .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (05) :3373-3387

[7] Uniqueness of solution for boundary value problems for fractional differential equations [J].

Cui, Yujun .

APPLIED MATHEMATICS LETTERS, 2016, 51 :48-54

[8] Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrodinger-Maxwell equations [J].

D'Aprile, T ;

Mugnai, D .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2004, 134 :893-906

[9]

Debnath L., 2003, Int. J. Math. Math. Sci, V2003, P30

[10] Positive solutions of the nonlinear Schrodinger equation with the fractional Laplacian [J].

Felmer, Patricio ;

Quaas, Alexander ;

Tan, Jinggang .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2012, 142 (06) :1237-1262

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