## DAVID STOLNICKI

PhD Graduate**PhD program:**: XXXV

**supervisor**: A. Pisante

**Thesis title:**Existence and qualitative proprieties of positive solutions of a class of fully nonlinear elliptic equations

We study existence and nonexistence of positive radial 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. We also present a symmetry
result for exterior domains under some decay assumptions.

**Research products**

- 11573/1598865 - 2021 - On a class of fully nonlinear elliptic equations in dimension two (01a Articolo in rivista)

PACELLA, FILOMENA; STOLNICKI, DAVID - 11573/1670844 - 2023 - Existence and qualitative proprieties of positive solutions of a class of fully nonlinear elliptic equations (07a Tesi di Dottorato)

STOLNICKI, DAVID