Positive solutions for a system of nonlinear singular Hammerstein integral equations via nonnegative matrices and applications

被引：16

作者：

Yang, Zhilin ^{[1
]}

Zhang, Zhitao ^{[2
]}

机构：

[1] Qingdao Technol Univ, Dept Math, Qingdao 266033, Shandong, Peoples R China

[2] Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

POSITIVITY | 2012年 / 16卷 / 04期

关键词：

System of nonlinear Hammerstein integral equations; Positive solution; R-+(n)-monotone matrix; Elliptic system; Positive radial solution; CONSTANT-SIGN SOLUTIONS; BOUNDARY-VALUE-PROBLEMS; REFLEXIVE BANACH-SPACES; MULTIPLICITY; EXISTENCE; FREDHOLM; EIGENVALUES;

D O I：

10.1007/s11117-011-0146-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are concerned with the existence and multiplicity of positive solutions for the system of nonlinear singular Hammerstein integral equations u(i)(t) = integral(b)(a)k(i)(t, s)g(i)(s)f(i)(s, u(1)(s),..., u(n)(s))ds, i = 1, 2,..., n. We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing nonnegative matrices. As applications, the main results are applied to establish the existence and multiplicity of positive solutions for an elliptic system in an annulus.

引用

页码：783 / 800

页数：18

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