Uniqueness of positive radial solutions for quasilinear elliptic equations in an annulus

Abstract

Extending a previous result of Tang [1] we prove the uniqueness of positive radial solutions of Δ p u + f ( u ) = 0 , subject to Dirichlet boundary conditions on an annulus in R n with 2 < p ≤ n , under suitable hypotheses on the nonlinearity f . This argument also provides an alternative proof for the uniqueness of positive solutions of the same problem in a finite ball (see [9]), in the complement of a ball or in the whole space R n (see [10,3,11]).