Year: 2023
Type: preprint
Abstract: We prove existence of a positive radial solution to the Choquard equation $$-Δu +V u=(I_α\ast |u|^p)|u|^{p-2}u\qquad\text{in}\,\,\,Ω$$ with Neumann or Dirichlet boundary conditions, when $Ω$ is an annulus, or an exterior domain of the form $\mathbb{R}^N\setminus \bar{B}_a(0)$. We provide also a nonexistence result, that is if $p\ge\frac{N+α}{N-2}$ the corresponding Dirichlet problem does not have any nontrivial regular solution in strictly strictly star-shaped domains.
Source: arXiv (Cornell University)
Authors: Bernardini, Chiara, Cesaroni, Annalisa
Institution: University of Padua
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4376988581