Abstract

In this article we study uniqueness of positive solutions for the nonlinear uniformly elliptic equation Mλ, Λ + ( D2 u ) - u + up = 0 in RN, limr → ∞ u ( r ) = 0, where Mλ, Λ + ( D2 u ) denotes the Pucci's extremal operator with parameters 0 < λ {less-than or slanted equal to} Λ and p > 1. It is known that all positive solutions of this equation are radially symmetric with respect to a point in RN, so the problem reduces to the study of a radial version of this equation. However, this is still a nontrivial question even in the case of the Laplacian ( λ = Λ). The Pucci's operator is a prototype of a nonlinear operator in no-divergence form. This feature makes the uniqueness question specially challenging, since two standard tools like Pohozaev identity and global integration by parts are no longer available. The corresponding equation involving Mλ, Λ - is also considered. © 2005 Elsevier Inc. All rights reserved.