Monday, May 13, 2024 — 3:00 pm — aula M2.5, edificio Matematica
Radial positive solutions for a class of Neumann problems without growth conditions
Abstract: In this talk, I will give an overview of results obtained in collaboration with several authors in the past years, concerning existence of radial, positive solutions of the quasilinear equation
$$-\Delta_p u=f(u),\quad u>0 \textrm{ in }\Omega,\quad\partial_\nu u=0\textrm{ on }\partial\Omega.$$
Here $1<p<\infty$ and $\Omega\subset\mathbb R^N$ is either a ball or an annulus.
The nonlinearity $f$ is possibly supercritical in the sense of Sobolev embeddings; in particular, our assumptions allow to include the prototype nonlinearity $f(s)=-s^{p-1}+s^{q-1}$ for every $q>p$.