The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application

被引：136

作者：

Jiang, Daqing ^{[1
]}

Yuan, Chengjun ^{[1
,2
]}

机构：

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

[2] Harbin Univ, Sch Math & Comp, Harbin 150086, Heilongjiang, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 02期

关键词：

Riemann-Liouville's fractional derivative; Boundary value problem; Positive solution; Fixed point theorem in cones; EXISTENCE; UNIQUENESS;

D O I：

10.1016/j.na.2009.07.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss some new positive properties of the Green function for boundary value problems of nonlinear Dirichlet-type fractional differential equations. its applications are also given. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：710 / 719

页数：10

共 18 条

[1] Twin solutions to singular Dirichlet problems
Agarwal, RP
O'Regan, D
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 240 (02) : 433 - 445
[2] Formulation of Euler-Lagrange equations for fractional variational problems
Agrawal, OP
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 272 (01) : 368 - 379
[3] Positive solutions for boundary value problem of nonlinear fractional differential equation
Bai, ZB
Lü, HS
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 311 (02) : 495 - 505
[4] Existence and uniqueness for a nonlinear fractional differential equation
Delbosco, D
Rodino, L
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 204 (02) : 609 - 625
[5] Krasnoselskii MA., 1964, POSITIVE SOLUTIONS O
[6] Basic theory of fractional differential equations
Lakshmikantham, V.
Vatsala, A. S.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (08) : 2677 - 2682
[7] General uniqueness and monotone iterative technique for fractional differential equations
Lakshmikantham, V.
Vatsala, A. S.
[J]. APPLIED MATHEMATICS LETTERS, 2008, 21 (08) : 828 - 834
[8] Lakshmikantham V., 2007, Commun. Appl. Anal, V11, P395
[9] MULTIPLE POSITIVE FIXED-POINTS OF NON-LINEAR OPERATORS ON ORDERED BANACH-SPACES
LEGGETT, RW
WILLIAMS, LR
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1979, 28 (04) : 673 - 688
[10] Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations
Lin, Xiaoning
Jiang, Daqing
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 321 (02) : 501 - 514

← 1 2 →