No abstract

In this paper, we discuss the existence of positive solutions to the singular Dirichlet boundary value problems (BVPs) for ordinary differential equations (ODEs) of the formwhere a ∈ (-1, 0). The nonlinearity f (t, x, y) may be singular for the space variables x = 0 and/or y = 0. Moreover, since a = 0, the differential operator on the left-hand side of the differential equation is singular at t = 0. Sufficient conditions for the existence of positive solutions of the above BVPs are formulated and asymptotic properties of solutions are specified. The theory is illustrated by numerical experiments computed using the open domain MATLAB code bvpsuite, based on polynomial collocation.