Positive radial solutions to a 'semilinear' equation involving the Pucci's operator

Abstract

In this article we prove existence of positive radially symmetric solutions for the nonlinear elliptic equation A formula is presented. where Mλ,Λ+ denotes the Pucci's extremal operator with parameters 0 < λ ≤ Λ 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) γ = 1 and f (s) = sp, 1 < μ1+. Here p*+ is critical exponent for Mλ,Λ+ and μ1+, is the first eigenvalue of Mλ,Λ+ in BR. Analogous results are obtained for the operator Mλ,Λ-. © 2004 Published by Elsevier Inc.