In this talk we present some results concerning a class of fully nonlinear equations driven by the Pucci's operators, with a Dirichlet boundary condition, and with a power nonlinear term.This study is important to understand some invariance of the Pucci's operators which may be not so evident by their definition. Indeed, though these problems do not have a variational structure (as it happens for the classical Lane-Emden problem), some critical exponents in connection with the existence of solutions and some concentration phenomena appear.
Dipartimento di Matematica, Università degli Studi di Torino