Existence and qualitative proprieties of positive solutions of a class of fully nonlinear elliptic equations

We study existence and nonexistence of radial positive solutions for a class of fully nonlinear equations involving Pucci’s extremal operators. By analyzing the periodic orbits of an associated dynamical system we are able to give estimates on the range of the exponents for which entire oscillating solutions exist. In dimensions greater or equal than three our results improve the previously known bounds while in dimension 2 we prove the existence of a critical exponent. It is also presented a symmetry result for exterior domains under some decay assumptions.