Asymptotic behavior of ground states of generalized pseudo-relativistic Hartree equation

Article type: Research Article

Authors: Belchior, P.^a | Bueno, H.^b | Miyagaki, O.H.^{c; *} | Pereira, G.A.^b

Affiliations: [a] Pontifícia Universidade Católica, Departamento de Matemática, Av Dom José Gaspar, 500 – Coração Eucarístico, 30535-901 Belo Horizonte – MG, Brazil. E-mail: pedrobelchior18@gmail.com | [b] Departmento de Matemática, Universidade Federal de Minas Gerais, 31270-901 – Belo Horizonte – MG, Brazil. E-mails: hamilton.pb@gmail.com, gilbertoapereira@yahoo.com.br | [c] Departmento de Matemática, Universidade Federal de Juiz de Fora, 36036-330 – Juiz de Fora – MG, Brazil. E-mail: ohmiyagaki@gmail.com

Correspondence: [*] Corresponding author. E-mail: ohmiyagaki@gmail.com.

Abstract: With appropriate hypotheses on the nonlinearity f, we prove the existence of a ground state solution u for the problem −Δ+m2u+Vu=(W∗F(u))f(u)in RN, where V is a bounded potential, not necessarily continuous, and F the primitive of f. We also show that any of this problem is a classical solution. Furthermore, we prove that the ground state solution has exponential decay.

Keywords: Variational methods, exponential decay, fractional Laplacian, Hartree equations

DOI: 10.3233/ASY-191561

Journal: Asymptotic Analysis, vol. 118, no. 4, pp. 269-295, 2020