This paper is devoted to the problem of existence of solutions to the nonlinear singular two point boundary value problem
, withy satisfying either “mixed” boundary datay(1)=Limy?0+p(t)y'(t)=0 or “dirichlet” boundary datay(0)=y(1)=0. Throughout our nonlinear termqf is allowed to be singular att=0,t=1,y=0 and/orpy'=0.
We investigate some properties of nonlinear integral operators of Urysohn--Stieltjes type with kernels depending on two variables.
Results concerning the continuity and compactness of these operators are obtained. The solvability of nonlinear Urysohn--Stieltjes
integral equations is also studied.