Radial solutions of equations and inequalities involving the <inline-formula><graphic file="1029-242X-1997-409301-i1.gif"/></inline-formula>-Laplacian

Abstract

Several problems for the differential equation are considered. For , the operator is the radially symmetric -Laplacian in . For the initial value problem with given data various uniqueness conditions and counterexamples to uniqueness are given. For the case where is increasing in , a sharp comparison theorem is established; it leads to maximal solutions, nonuniqueness and uniqueness results, among others. Using these results, a strong comparison principle for the boundary value problem and a number of properties of blow-up solutions are proved under weak assumptions on the nonlinearity .

Keywords

• <it>p</it>-Laplacian
• radial solutions
• uniqueness
• comparison principle
• blow-up solutions