Abstract

In this article we study some results on the existence of radially symmetric, non-negative solutions for the nonlinear elliptic equation M ?,?+(D2u)+up = 0inRN. Here N?3, p > 1 and M?,?+ denotes the Pucci's extremal operators with parameters 0<? ? ?. The goal is to describe the solution set in function of the parameter p. We find critical exponents 1<p *+<pp+ that satisfy: (i) If 1<p<p*+ then there is no non-trivial radial solution of (*). (ii) If p = p*+ then there is a unique fast decaying radial solution of (*). (iii) If p*+<p ? pp+ then there is a unique pseudo-slow decaying radial solution to (*). (iv) If pp+<p then there is a unique slow decaying radial solution to (*). Similar results are obtained for the operator M?,?-. © 2003 Éditions scientifiques et médicales Elsevier SAS.