Uniqueness of positive solutions of quasilinear differential equations

Abstract

In this paper we are concerned with the uniqueness of positive solutions of boundary value problems for quasilinear differential equations of the type $(|u'|^{m-2}u')' + p(t)f(u) = 0, $ $ m>1$. The key ingredient of the method is the generalized Prüfer transformation. These problems arise, for example, in the study of the $m$-Laplace equation in annular regions.