Instituto de Matemática e Estatística
Universidade de São Paulo
Rua do Matão, 1010
05508-090 São Paulo SP, Brazil
email: gpramos@icmc.usp.br
Gustavo de Paula Ramos
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.
DOI: 10.58997/ejde.2025.29
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Gustavo de Paula Ramos Instituto de Matemática e Estatística Universidade de São Paulo Rua do Matão, 1010 05508-090 São Paulo SP, Brazil email: gpramos@icmc.usp.br |
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