Positive Solutions for a Class of Coupled System of Singular Three-Point Boundary Value Problems

Existence of positive solutions for a coupled system of nonlinear three-point boundary value problems of the type -x[variant prime][variant prime] (t)=f(t,x(t),y(t)) , t∈(0,1) , -y[variant prime][variant prime] (t)=g(t,x(t),y(t)) , t∈(0,1) , x(0)=y(0)=0 , x(1)=αx(η) , y(1)=αy(η) , is established. The nonlinearities f , g:(0,1)×(0,∞)×(0,∞)[arrow right][0,∞) are continuous and may be singular at t=0,t=1,x=0 , and/or y=0 , while the parameters η , α satisfy η∈(0,1),0