Monday, May 13, 2024 — 3:45 pm — aula M2.5, edificio Matematica
Multiple nonradial solutions for a supercritical problem in an exterior domain
Abstract: In this talk, I will present an existence result for the Dirichlet problem associated with the elliptic equation
$$-\Delta u + u = a(x)|u|^{p-2}u$$
set in an annulus or an exterior domain of $\mathbb R^N$, $N \geq 3$. Here $p>2$ is allowed to be supercritical in the sense of Sobolev embeddings, and $a(x)$ is a positive weight with additional symmetry and monotonicity properties.
In the special case of radial weight $a(x)$, such an existence result ensures the multiplicity of nonradial solutions.
This is joint work with Alberto Boscaggin (Università di Torino), Benedetta Noris (Politecnico di Milano), and Tobias Weth (Goethe-Universitat Frankfurt).