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

Positive solutions for a system of nonlinear singular Hammerstein integral equations via... We are concerned with the existence and multiplicity of positive solutions for the system of nonlinear singular Hammerstein integral equations $$u_i(t)=\int_a^bk_i(t,s)g_i(s)f_i(s,u_1(s),\ldots,u_n(s)) {\rm d} s,\quad i=1,2,\ldots,n.$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

Positivity, Volume 16 (4) – Oct 13, 2011
18 pages

Publisher
Springer Journals
Subject
Mathematics; Potential Theory; Operator Theory; Fourier Analysis; Econometrics; Calculus of Variations and Optimal Control; Optimization
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-011-0146-4
Publisher site
See Article on Publisher Site

### Abstract

We are concerned with the existence and multiplicity of positive solutions for the system of nonlinear singular Hammerstein integral equations $$u_i(t)=\int_a^bk_i(t,s)g_i(s)f_i(s,u_1(s),\ldots,u_n(s)) {\rm d} s,\quad i=1,2,\ldots,n.$$ 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.

### Journal

PositivitySpringer Journals

Published: Oct 13, 2011

### References

• Constant-sign solutions of a system of Fredholm integral equations
Agarwal, R.P.; O’Regan, D.; Wong, P.J.Y.
• Constant-sign solutions of a system of integral equations: the semipositone and singular case
Agarwal, R.P.; O’Regan, D.; Wong, P.J.Y.

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