Abstract

In this article we prove existence of positive radially symmetric solutions for the nonlinear elliptic equation A formula is presented. where M?,?+ denotes the Pucci's extremal operator with parameters 0 < ? ? ? and BR is the ball of radius R in RN, N ? 3. The result applies to a wide class of nonlinear functions f, including the important model cases: (i) ? = 1 and f (s) = sp, 1 <p <p*+. (ii) ? = 0, f (s) = ?s + sp, 1 <p <p*+ and 0 ? ? < ?1+. Here p*+ is critical exponent for M?,?+ and ?1+, is the first eigenvalue of M?,?+ in BR. Analogous results are obtained for the operator M?,?-. © 2004 Published by Elsevier Inc.