Published Paper
Inserted: 17 may 2023
Last Updated: 7 feb 2025
Journal: Nonlinear Analysis
Volume: 254
Year: 2025
Doi: 10.1016/j.na.2024.113745
Abstract:
We prove existence of a positive radial solution to the Choquard equation
\[-\Delta u +V u=(I_\alpha\ast
u
^p)
u
^{p-2}u\qquad\text{in}\,\,\,\Omega\]
with Neumann or Dirichlet boundary conditions, when $\Omega$ 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 $p\ge\frac{N+\alpha}{N-2}$ the
corresponding Dirichlet problem does not have any nontrivial regular solution
in strictly strictly star-shaped domains.