Remarks about a generalized pseudo-relativistic Hartree equation

Abstract

With appropriate hypotheses on the nonlinearity $f$, we prove the existence of a ground state solution $u$ for the problem \[(-Δ+m^2)^σu+Vu=\left(W*F(u)\right)f(u)\ \ \text{in }\ \mathbb{R}^{N},\] where $0<\sigma <1$, $V$ is a bounded continuous potential and $F$ the primitive of $f$. We also show results about the regularity of any solution of this problem.

29 pages. arXiv admin note: text overlap with arXiv:1802.03963