On critical exponents for Lane-Emden-Fowler-type equations with a singular extremal operator

Abstract

In this article, we consider the nonlinear elliptic equation vertical bar del mu vertical bar(beta) M-lambda,Lambda(+) (D(2)u) + u(P) = 0 in R-N. Here, M-lambda,Lambda(+) denotes Pucci's extremal operator with parameters Lambda >= lambda >0 and -1 < beta < 0.We prove the existence of a critical exponent p(+)(*) that determines the range of for which we have the existence or nonexistence of a positive radial solution to (*). In addition, we describe the solution set in terms of the parameter p and find two new critical exponents 1 < p(+)(*) < <(p)over tilde>(beta) for the equation (*), where the solution set sharply changes its qualitative properties when the value of p exceeds these critical exponents.