Uniqueness of positive radially symmetric solutions for a Schrödinger–Poisson–Slater equation
Year: 2026
Type: article
Abstract: The paper deals with radially symmetric solutions of the following nonlinear Schrödinger–Poisson–Slater equation − Δ u + | x | − 1 ∗ u 2 u = μ | u | p − 2 u , i n R 3 , $${-}{\Delta }u+\left(\vert x{\vert }^{-1}\ast {u}^{2}\right)u=\mu \vert u{\vert }^{p-2}u,\enspace \mathrm{i}\mathrm{n}\enspace {\mathbb{R}}^{3},$$ where (| x | −1 ∗ u 2 ) is the repulsive Coulomb potential and μ > 0 is the Slater constant. When p = 18/5, we prove that the radially symmetric ground state solution of above equation is unbroken. Then, we obtain the uniqueness and smoothness of this positive radially symmetric solution and determine the expression for the best constant of the Coulomb–Sobolev inequality.
Source: Advanced Nonlinear Studies
Authors: Chunyu Lei, Zhisu Liu, Patrizia Pucci, Binlin Zhang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,469
OpenAlex ID: W7161550125