Abstract

In this Note we present some results on the existence of radially symmetric solutions for the nonlinear elliptic equation M?,+? (D2u +uP =0, u ? 0 in ?N. Here N ? 3, p > 1 and M?,+? denotes the Pucci's extremal operators with parameters 0 < ? ? ?. The goal is to describe the solution set as function of the parameter p. We find critical exponents 1 < p+s < p+* < p+p, that satisfy: (i) If 1 < p < p+* then there is no nontrivial solution of (*). (ii) If p = p+* then there is a unique fast decaying solution of (*). (iii) If p* < p ? p+p then there is a unique pseudo-slow decaying solution to (*). (iv) If p+p < p then there is a unique slow decaying solution to (*). Similar results are obtained for the operator M?,-?. © 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.