The solution for a class of sum operator equation and its application to fractional differential equation boundary value problems

被引：23

作者：

Wang, Hui ^{[1
]}

Zhang, Lingling ^{[1
]}

机构：

[1] Taiyuan Univ Technol, Coll Math, Yingze West Rd, Taiyuan 030024, Shanxi, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2015年

基金：

中国国家自然科学基金;

关键词：

operator equation; fixed point theorem; fractional differential equation; positive solution; MONOTONE POSITIVE SOLUTIONS; FIXED-POINT THEOREMS; EIGENVALUE PROBLEMS; EXISTENCE; UNIQUENESS;

D O I：

10.1186/s13661-015-0467-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a class of sum operator equation Ax + Bx + C(x,x) = x on ordered Banach spaces, where A is an increasing operator, B is a decreasing operator, and C is a mixed monotone operator. The existence and uniqueness of its positive solution are obtained by using the properties of cone and fixed point theorems for mixed monotone operators. As an application, we utilize the obtained results to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.

引用

页码：1 / 16

页数：16

共 24 条

[1] A multiplicity result for second order impulsive differential equations via the Leggett Williams fixed point theorem [J].

Agarwal, RP ;

O'Regan, D .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 161 (02) :433-439

[2] Monotone positive solutions for a fourth order equation with nonlinear boundary conditions [J].

Alves, Edson ;

Ma, To Fu ;

Pelicer, Mauricio Luciano .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (09) :3834-3841

[3] FIXED-POINT EQUATIONS AND NONLINEAR EIGENVALUE PROBLEMS IN ORDERED BANACH-SPACES [J].

AMANN, H .

SIAM REVIEW, 1976, 18 (04) :620-709

[4] Three positive fixed points of nonlinear ordered Banach spaces [J].

Avery, RI ;

Peterson, AC .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2001, 42 (3-5) :313-322

[5] Three symmetric positive solutions for a second-order boundary value problem [J].

Avery, RI ;

Henderson, J .

APPLIED MATHEMATICS LETTERS, 2000, 13 (03) :1-7

[6] 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

[7] Positive fixed points for a class of nonlinear operators and applications [J].

Berzig, Maher ;

Samet, Bessem .

POSITIVITY, 2013, 17 (02) :235-255

[8] Stability of positive fixed points of nonlinear operators [J].

Chen, YZ .

POSITIVITY, 2002, 6 (01) :47-57

[9]

Deimling K., 1985, Nonlinear Functional Analysis

[10] Existence of positive solutions to an arbitrary order fractional differential equation via a mixed monotone operator method [J].

Jleli, Mohamed ;

Samet, Bessem .

NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2015, 20 (03) :367-376

← 1 2 3 →