We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet, \(\delta \), or \(\delta '\) boundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is based on the argument by Murphy and Nakanishi (Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations), who treated the long-range nonlinear Schrödinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions.

中文翻译：

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星图上具有长期非线性的Schrödinger方程对驻波的散射失败

我们考虑星图上具有幂型远程非线性的Schrödinger方程。在顶点的一般边界条件下，包括Kirchhoff，Dirichlet，\（\ delta \）或\（\ delta'\）边界条件，我们证明了非平凡的整体解不会散射到驻波。我们的证明基于Murphy和Nakanishi的论点（对于远程非线性Schrödinger方程，散射到孤立波的失败），他们考虑了欧几里德空间中具有一般势的远程非线性Schrödinger方程，以便考虑一般边界条件。