With appropriate hypotheses on the nonlinearity $f$, we prove the existence of a ground state solution $u$ for the problem \[\sqrt{-\Delta+m^2}\, u+Vu=\left(W*F(u)\right)f(u)\ \ \text{in }\ \mathbb{R}^{N},\] 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.

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广义伪相对论Hartree方程基态的渐近行为

通过对非线性 $f$ 的适当假设，我们证明了问题 \[\sqrt{-\Delta+m^2}\, u+Vu=\left(W*F (u)\right)f(u)\ \ \text{in }\ \mathbb{R}^{N},\] 其中 $V$ 是有界势，不一定连续，$F$ 是$f$。我们还表明，这个问题中的任何一个都是经典的解决方案。此外，我们证明了基态解具有指数衰减。