论文标题
NLSE在3D中具有点缺陷的基态的存在，结构和鲁棒性
Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect
论文作者
论文摘要
我们研究了Schrödinger方程的基础状态，并在第三维度中进行了焦点非线性和点相互作用。我们确定质量的每个价值都存在基态。此外，它们是正面的，径向对称，沿着径向的方向减小，并在点相互作用的位置显示出库仑的奇异性。值得注意的是，基态的存在与点相互作用的有吸引力或排斥性无关。
We study the ground states for the Schrödinger equation with a focusing nonlinearity and a point interaction in dimension three. We establish that ground states exist for every value of the mass; moreover they are positive, radially symmetric, decreasing along the radial direction, and show a Coulombian singularity at the location of the point interaction. Remarkably, the existence of the ground states is independent of the attractive or repulsive character of the point interaction.
