On the Existence of Positive Solutions of a Singular Nonlinear Differential Equation

We consider the nonlinear singular differential equation 1 A Au − μu = −σf · u on 0 ω ω ∈ 0 ∞ where μ and σ are two positive Radon measures on 0 ω not charging points. For a regular function f and under some hypotheses on A, we prove the existence of an infinite number of nonnegative solutions. Our approach is based on the use of the Green’s function of the homogeneous equation and Schauder’s fixed-point theorem.