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.
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页码：783 / 800
页数：18
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