We deal with a class of magnetic pseudo-relativistic Hartree type equation $\sqrt{(-i\mathrm{\nabla }-A(x){)}^2+m^2}u+W\left(x\right)u=(I_{\alpha }\ast |u{|}^p)|u{|}^{p-2}u,x\in {\mathbb{R}}^N,$ where $N\ge 3$, m>0, $A:{\mathbb{R}}^N\to {\mathbb{R}}^N$ is a continuous vector potential, $W:{\mathbb{R}}^N\to \mathbb{R}$ is an external continuous scalar potential and $I_{\alpha }\left(x\right)=\left(c_{N,\alpha }/|x{|}^{N-\alpha }\right)(x\ne 0)$ is a convolution kernel, $c_{N,\alpha }>0$ is a positive constant, $2\le p<2N/\left(N-1\right)$, $(N-1)p-N<\alpha <N$. Under the action of some subgroup of linear isometries on potential A and W, and some assumptions on the decay of A and W at infinity, we prove the existence of vortex-type solutions to this problem by using variational methods and asymptotic estimates as p = 2.

我们处理一类磁伪相对论 Hartree 型方程$\sqrt{(-\mathrm{一世}\mathrm{\nabla }-\mathrm{一种}(X){)}^2+{米}^2}你+W\left(X\right)你=({\mathrm{一世}}_{\alpha }*|你{|}^p)|你{|}^{p-2}你,X\in {\mathbb{R}}^{ñ},$在哪里$ñ\ge 3$, m >0,$\mathrm{一种}：{\mathbb{R}}^{ñ}\to {\mathbb{R}}^{ñ}$是一个连续向量势，$W：{\mathbb{R}}^{ñ}\to \mathbb{R}$是外部连续标量势和${\mathrm{一世}}_{\alpha }\left(X\right)=\left(C_{ñ,\alpha }/|X{|}^{ñ-\alpha }\right)(X\ne 0)$是一个卷积核，$C_{ñ,\alpha }>0$是一个正常数，$2\le p<2ñ/\left(ñ-1\right)$,$(ñ-1)p-ñ<\alpha <ñ$. 在一些线性等距子群对势A和W的作用下，以及对A和W在无穷远处衰减的一些假设下，我们利用变分方法和渐近估计证明了该问题存在涡型解，因为p  = 2.