We present recent results about radial solutions of a class of fully nonlinear elliptic Dirichlet problems posed in a ball, driven by the extremal Pucci's operators and provided with power zero order terms. We show that a new critical exponent appears, related to the existence or nonexistence of sign-changing solutions. Furthermore we analyze the new concentration phenomena occurring as the exponents approach the critical values. Based on joint works with A. Iacopetti, G. Galise and F. Pacella.