论文标题
站立波对非线性schrödinger方程的存在和轨道稳定性，半线的平方电势逆向
Existence and orbital stability of standing waves to a nonlinear Schrödinger equation with inverse square potential on the half-line
论文作者
论文摘要
我们研究了在半线上具有反方势的非线性schrödinger方程的遗传波的性质。我们首先建立了站着波浪的存在。然后，通过对基态的各种表征，我们建立了驻质量亚临界非线性的驻波轨道稳定性。由于问题的非紧密度和缺乏问题的不变性，因此我们应用了一个配置文件分解参数。我们通过将问题与“无穷大”（即无平方势的方程式）进行比较，从而获得收敛最小化序列。最后，我们通过对质量超临界非线性的爆炸论点来建立轨道不稳定。
We investigate the properties of standing waves to a nonlinear Schrödinger equation with inverse-square potential on the half-line. We first establish the existence of standing waves. Then, by a variational characterization of the ground states, we establish the orbital stability of standing waves for mass sub-critical nonlinearity. Owing to the non-compactness and the absence of translational invariance of the problem, we apply a profile decomposition argument. We obtain convergent minimizing sequences by comparing the problem to the problem at "infinity" (i.e., the equation without inverse square potential). Finally, we establish orbital instability by a blow-up argument for mass super-critical nonlinearity.
