Existence of positive solutions of second order singular nonlinear eigenvalue problems

Abstract:

In this paper, we consider the existence of positive solutions for the second-order singular differential equation with Sturm-Liouville boundary condition. By dividing the growth property of f at zero and infinity into 9 cases, we discuss the range of parameter corresponding to the cases of the equation having none, at least one and two positive solutions by using the fixed point theorem of cone expansion and compression.