Singular mixed boundary value problem

AbstractWe study singular boundary value problems with mixed boundary conditions of the formu″+f(t,u,u′)=0,u′(0)=0,u(T)=0, where [0,T]⊂R, D=(0,∞)×(−∞,0), f is a nonnegative function and satisfies the Carathéodory conditions on (0,T)×D. Here, f can have a time singularity at t=0 and/or t=T and a space singularity at x=0 and/or y=0. We present conditions for the existence of solutions positive on [0,T) and having continuous first derivatives on [0,T]