New concentration phenomena for radial sign-changing solutions of fully nonlinear elliptic equations

Abstract

We present recent results about radial sign-changing 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 new critical exponents appear, related to the existence or nonexistence of sign-changing solutions and due to the fully nonlinear character of the considered problem. Furthermore, we analyze the new concentration phenomena occurring as the exponents approach the critical values.

Keywords

• pucci's extremal operators
• sign-changing radial solutions
• new critical exponents