标题： 非均匀Abelian-Higgs模型中BPS真空和多涡旋的存在性与唯一性 显示英文标题

标题： Existence and Uniqueness of BPS Vacuum and Multi-vortices in Inhomogeneous Abelian Higgs Model

摘要： 非均匀规范的Higgs模型的BPS极限在$(1+2)$维中被考虑。 在存在由空间坐标表示的非均匀性的情况下，研究了二阶Bogomolny方程。 假设非均匀函数的$L^{2}(\mathbb{R}^{2})$范数有一个合理的上限，我们证明了零能量的非平凡BPS真空解以及量子化的正能拓扑BPS多涡旋解的存在性和唯一性。 显示英文摘要

摘要： The BPS limit of the inhomogeneous abelian Higgs model is considered in $(1+2)$-dimensions. The second order Bogomolny equation is examined in the presence of an inhomogeneity expressed as a function of spatial coordinates. Assuming a physically reasonable upper bound on the $L^{2}(\mathbb{R}^{2})$ norm of the inhomogeneity function, we prove the existence and the uniqueness of nontrivial BPS vacuum solution of zero energy and topological BPS multi-vortex solutions of quantized positive energies.