The existence of a ground state solution for a class of fractional differential equation with p-Laplacian operator

被引：3

作者：

Hu, Zhigang ^{[1
]}

Liu, Wenbin ^{[1
]}

Chen, Taiyong ^{[1
]}

机构：

[1] China Univ Min & Technol, Dept Math, Xuzhou 221008, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2016年

关键词：

fractional differential equations; boundary value problem; Nehari manifold; ground state solution; BOUNDARY-VALUE-PROBLEMS; POSITIVE SOLUTIONS;

D O I：

10.1186/s13661-016-0557-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we apply the Nehari manifold method to study the fractional p-Laplacian differential equation {D-t(T)alpha phi(p)((0)D(t)(alpha)u(t)) = f (t, u(t)), t is an element of [0, T], u(0) = u(T) = 0, where D-0(t)alpha, D-t(T)alpha are the left and right Riemann-Liouville fractional derivatives of order 0 <= alpha < 1, respectively. We prove the existence of a ground state solution for the boundary value problem.

引用

页码：1 / 12

页数：12

共 28 条

[1] Positive solutions for Dirichlet problems, of singular nonlinear fractional differential equations [J].

Agarwal, Ravi P. ;

O'Regan, Donal ;

Stanek, Svatoslav .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 371 (01) :57-68

[2] A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions [J].

Agarwal, Ravi P. ;

Benchohra, Mouffak ;

Hamani, Samira .

ACTA APPLICANDAE MATHEMATICAE, 2010, 109 (03) :973-1033

[3] Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions [J].

Ahmad, Bashir ;

Nieto, Juan J. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (09) :1838-1843

[4]

[Anonymous], 1981, Ann. Fac. Sci. Toulouse Math.

[5]

[Anonymous], 2006, Journal of the Electrochemical Society

[6]

Bai C, 2012, ELECTRON J DIFFER EQ, V2012, P176

[7] Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem [J].

Bai, Chuanzhi .

ABSTRACT AND APPLIED ANALYSIS, 2012,

[8] Positive solutions for boundary value problem of nonlinear fractional differential equation [J].

Bai, ZB ;

Lü, HS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 311 (02) :495-505

[9] The existence of solutions for a fractional multi-point boundary value problem [J].

Bai, Zhanbing ;

Zhang, Yinghan .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (08) :2364-2372

[10] Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory [J].

Chen, Jing ;

Tang, X. H. .

ABSTRACT AND APPLIED ANALYSIS, 2012,

← 1 2 3 →