A singular ODE related to quasilinear elliptic equations

Abstract

We consider a quasilinear elliptic problem with the natural growth in the gradient. Existence, non-existence, uniqueness, and qualitative properties of positive solutions are obtained. We consider both weak and strong solutions. All results are based on the study of a suitable singular ODE of the first order. We also introduce a comparison principle for a class of nonlinear integral operators of Volterra type that enables to obtain uniqueness of weak solutions of the quasilinear equation.

Keywords

• p-Laplacian
• spherically symmetric
• existence
• non-existence
• uniqueness
• comparison principle
• singular ODE
• regularity.