Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 29, pp. 1-10.

Title: Asymptotic profile of least energy solutions to the nonlinear Schrodinger-Bopp-Podolsky system

Author: Gustavo de Paula Ramos (Univ. de Sao Paulo, SP, Brazil)
  
Abstract:
We consider the  nonlinear Schrodinger-Bopp-Podolsky system in 
$\mathbb{R}^3$:
$$\displaylines{
- \Delta v + v + \phi v = v |v|^{p - 2}, \cr
\beta^2 \Delta^2 \phi - \Delta \phi = 4 \pi v^2,
}$$
where $\beta > 0$ and $3 < p < 6$; the unknowns being
$v$ and $\phi \colon \mathbb{R}^3 \to \mathbb{R}$.
We prove that, as
$\beta \to 0$ and up to translations and subsequences, 
the least energy solutions of the above converge to a least energy 
solution to the  nonlinear Schrodinger-Poisson system in
$\mathbb{R}^3$:
$$\displaylines{
- \Delta v + v + \phi v = v |v|^{p - 2}, \cr
- \Delta \phi = 4 \pi v^2.
}$$


Submitted January 2, 2025. Published March 17, 2025.
Math Subject Classifications: 35J61, 35B40, 35Q55, 45K05.
Key Words: Schrodinger-Bopp-Podolsky system; Schrodinger-Poisson system;
 nonlocal semilinear elliptic problem; variational methods;  ground state; 
 Nehari-Pohozaev manifold; Concentration-compactness.