On the Uniqueness of Positive Solutions of a Quasilinear Equation Containing a Weighted p-Laplacian, the Superlinear Case

Abstract

We consider the problem of uniqueness of positive solutions to boundary value problems containing the equation: -\Delta_p u =K(|x|)f(u), p>1. f is positive, is locally Lipschitz and satisfies some superlinear growth condition after u_0, a zero of f before which it is non positive and not identically 0. We show that the Sturmnian theory arguments used by Coffman and Kwong are valid for the equation containing the p-Laplacian operator, even though they were thought to be unextendable beyond the semilinear equation. We obtain a monotone separation result which finally yields the desired uniqueness results.