Existence and Nonexistence of Positive Solutions to a Singular $p$-Laplacian Differential Equation

Abstract:

      In this paper we give a necessary and sufficient condition for the existence of positive solutions for the one-dimensional singular $p$-Laplacian differential equation. The methods used to show existence rely on upper-lower solutions method and compactness techniques, while the methods used to prove nonexistence are based on monotone techniques and scaling arguments.