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 M-lambda,Delta(+)(D(2)u) - gammau + f(u) = 0 in B-R, u = 0 on partial derivativeB(R), where M-lambda,Delta(+) denotes the Pucci's extremal operator with parameters 0<lambdaless than or equal toLambda and B-R is the ball of radius R in R-N, Ngreater than or equal to3. The result applies to a wide class of nonlinear functions f, including the important model cases: (i) gamma = 1 and f(s) = s(p), 1<p<p(*)(+). (ii) gamma = 0, f (s) = alphas +s(p), 1<p<p(*)(+) and 0less than or equal toalpha<mu(1)(+). Here p(*)(+) is critical exponent for M-lambda,Lambda(+) and mu(1)(+) is the first eigenvalue of M-lambda,Lambda(+) in B-R. Analogous results are obtained for the operator M-lambda,Lambda(-).