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  • Author or Editor: D. O'Regan x
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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.

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General existence criteria are presented for nonlinear singular boundary value problems. Our nonlinearity may be singular in both the dependent and independent variable.

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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.

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