Abstract
We consider the following system of integral equations u i (t)=μ∫ 0 1 g i (t,s)f(s,u 1 (s),u 2 (s),…,u n (s)) ds, t∈(0,1), 1≤i≤n, where μ>0, the function f may take negative values and f(·,u 1 ,u 2 ,…,u n ) may be singular at u j =0, j∈{1,2,…,n}. Our aim is to establish criteria such that the above system has a constant-sign solution. To illustrate the generality of the results obtained, application to a well known boundary value problem is included. We also extend the above problem to that on the half-line (0,∞) u i (t)=μ∫ 0 ∞ g i (t,s)f(s,u 1 (s),u 2 (s),…,u n (s)) ds, t∈(0,∞), 1≤i≤n.
Journal
Asymptotic Analysis
– IOS Press
Published: Jan 1, 2005