论文标题
NLSE的不连续基态在$ \ mathbb {r} $上与fülöp-tsutsui $δ$互动
Discontinuous Ground States for NLSE on $\mathbb{R}$ with a Fülöp-Tsutsui $δ$ interaction
论文作者
论文摘要
我们分析了具有聚焦功率非线性和位于原点的缺陷的一维非线性schrödinger方程的基态的存在和稳定性。在本文中，基态定义为在Nehari歧管上功能的动作功能的全球最小化器，所考虑的缺陷是fülöp-tsutsui $δ$类型，即$δ$条件，允许不连续。基态的存在是通过变异技术证明的，而稳定性是由Grillakis-Shatah-Strauss理论产生的。
We analyse the existence and the stability of the ground states of the one-dimensional nonlinear Schrödinger equation with a focusing power nonlinearity and a defect located at the origin. In this paper a ground state is defined as a global minimizer of the action functional on the Nehari manifold and the defect considered is a Fülöp-Tsutsui $δ$ type, namely a $δ$ condition that allows discontinuities. The existence of ground states is proved by variational techniques, while the stability results from the Grillakis-Shatah-Strauss theory.
