EXISTENCE RESULTS FOR FRACTIONAL BOUNDARY VALUE PROBLEM VIA CRITICAL POINT THEORY

被引：198

作者：

Jiao, Feng ^{[1
]}

Zhou, Yong ^{[2
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 04期

基金：

美国国家科学基金会;

关键词：

Fractional differential equations; boundary value problem; critical point theory; weak and strong solutions; DIFFERENTIAL-EQUATIONS; ORDER; DISPERSION; UNIQUENESS;

D O I：

10.1142/S0218127412500861

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, by the critical point theory, the boundary value problem is discussed for a fractional differential equation containing the left and right fractional derivative operators, and various criteria on the existence of solutions are obtained. To the authors' knowledge, this is the first time, the existence of solutions to the fractional boundary value problem is dealt with by using critical point theory.

引用

页数：17

共 41 条

[1] 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

[2] Formulation of Euler-Lagrange equations for fractional variational problems [J].

Agrawal, OP .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 272 (01) :368-379

[3]

[Anonymous], 2000, Applications of Fractional Calculus in Physics

[4]

[Anonymous], 1993, INTRO FRACTIONAL CA

[5]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[6]

[Anonymous], 2006, Journal of the Electrochemical Society

[7]

[Anonymous], 1986, MINIMAX METHODS CRIT

[8] The Dual Action of Fractional Multi Time Hamilton Equations [J].

Baleanu, Dumitru ;

Golmankhaneh, Ali Khalili ;

Golmankhaneh, Alireza Khalili .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2009, 48 (09) :2558-2569

[9] Existence of Periodic Solution for a Nonlinear Fractional Differential Equation [J].

Belmekki, Mohammed ;

Nieto, Juan J. ;

Rodriguez-Lopez, Rosana .

BOUNDARY VALUE PROBLEMS, 2009,

[10] Boundary value problems for differential equations with fractional order and nonlocal conditions [J].

Benchohra, M. ;

Hamani, S. ;

Ntouyas, S. K. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (7-8) :2391-2396

← 1 2 3 4 5 →