We consider solitary waves with prescribed stellar mass for the pseudo-relativistic Hartree equation, which is known to describe the dynamics of pseudo-relativistic boson stars in the meanfield limit. This leads to the study of the following nonlocal elliptic equation $\sqrt{-\Delta +m^2}u-({\left|x\right|}^{-\gamma }\ast {\left|u\right|}^2)u=\mu u,x\in {\mathbb{R}}^3$under the normalized constraint ${\int }_{{\mathbb{R}}^3}{\left|\psi (t,x)\right|}^{2}dx=N,$where $\gamma \in (1,2)$, $m>0$, $N>0$ denotes the stellar mass of Boson stars and the frequency $\mu \in \mathbb{R}$ is unknown and appears as Lagrange multiplier. In contrast to the mass-subcritical case $\gamma \in (0,1)$ and mass-critical case $\gamma =1$, the corresponding pseudo-relativistic Hartree energy functional is always unbounded on the $L^2$ sphere for any $N>0$, we prove that the above problem admits at least one solution $u_N$, which is a ground state if $N$ or $m$ is sufficiently small. Furthermore, the stability of the corresponding solitary wave for the related time-dependent pseudo-relativistic Hartree equation is given. In addition, we also give an accurate description of the limiting behavior of $u_N$ as $N\to 0^{+}$ and $m\to 0^{+}$, respectively. The main contribution of this paper is to extend the main results in Guo and Zeng (2017), Lenzmann (2009) and Coti Zelati and Nolasco (2013) from long range potential case $\gamma \in (0,1]$ to short range potential case $\gamma \in (1,2)$.

我们为拟相对论性Hartree方程考虑具有规定恒星质量的孤波，该方程被描述为在均值场极限内描述拟相对论玻色子星的动力学。这导致对以下非局部椭圆方程的研究$\sqrt{-\Delta +{米}^2}ü-（{\left|X\right|}^{-\gamma }\ast {\left|ü\right|}^2）ü=\mu ü，X\in {\mathbb{[R}}^3$在归一化约束下 ${\int }_{{\mathbb{[R}}^3}{\left|\psi （Ť，X）\right|}^{2}dX=ñ，$哪里 $\gamma \in （\mathrm{1个}，2）$， $米>0$， $ñ>0$ 表示玻色子恒星的恒星质量和频率 $\mu \in \mathbb{[R}$未知，显示为拉格朗日乘数。与质量亚临界情况相反$\gamma \in （0，\mathrm{1个}）$ 和批判性案例 $\gamma =\mathrm{1个}$，相应的伪相对论Hartree能量函数在 ${\mathrm{大号}}^2$ 任何领域 $ñ>0$，我们证明上述问题至少允许一种解决方案 ${ü}_{ñ}$，如果是 $ñ$ 要么 $米$足够小。此外，给出了相关的时变伪相对论Hartree方程的相应孤波的稳定性。此外，我们还给出了有关限制行为的准确描述。${ü}_{ñ}$ 如 $ñ\to 0^{+}$ 和 $米\to 0^{+}$， 分别。本文的主要贡献是从长期潜在案例中扩展了Guo和Zeng（2017），Lenzmann（2009）以及Coti Zelati和Nolasco（2013）的主要结果$\gamma \in （0，\mathrm{1个}]$ 到短程潜在案例 $\gamma \in （\mathrm{1个}，2）$。