Multiple positive bound states for the subcritical NLS equation on metric graphs
Multiple positive bound states for the subcritical NLS equation on metric graphs
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度量图上亚临界 NLS 方程的多个正束缚态
DOI：
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发表时间：
2017
影响因子：
2.1
通讯作者：
P. Tilli
中科院分区：
文献类型：
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作者：
R. Adami;E. Serra;P. Tilli
考虑非紧度规图上具有亚临界聚焦功率非线性的薛定谔方程，证明了对于每条有限边，存在一个质量的阈值，超过这个阈值，存在一个正的束界态，它只在那条边达到最大值。这种束缚状态被描述为与NLS方程相关的能量泛函的极小化子，带有一个额外的约束(除了质量规定之外)：这需要在证明极小化子满足欧拉-拉格朗日方程时特别小心。因此，对于足够大的质量，图的每条有限边至少有一个正的束缚状态，由于它的极小性质，它是轨道稳定的。
We consider the Schrödinger equation with a subcritical focusing power nonlinearity on a noncompact metric graph, and prove that for every finite edge there exists a threshold value of the mass, beyond which there exists a positive bound state achieving its maximum on that edge only. This bound state is characterized as a minimizer of the energy functional associated to the NLS equation, with an additional constraint (besides the mass prescription): this requires particular care in proving that the minimizer satisfies the Euler–Lagrange equation. As a consequence, for a sufficiently large mass every finite edge of the graph hosts at least one positive bound state that, owing to its minimality property, is orbitally stable.