Regions of existence and uniqueness for singular nonlinear diffusion problems

This paper presents a novel approach for constructing the lower and upper boundaries of closed regions where solutions to the singular nonlinear diffusion problems '' y(x) + m/x y '(x) = f(x,y(x)), x is an element of (0,1], m >= 0, y '(0) = 0, Ay(1) + By '(1) = C, A > 0, B >= 0, C >= 0, exist. This existence result is proved using the method of lower and upper solutions with monotone iterative technique under the restriction that f(x, y)is continuous in x is an element of [0,1] and non-increasing in y in such regions. Additional uniqueness criteria is also established. The approach is illustrated on four singular nonlinear diffusion problems including some real life applications.