Abstract

We study the problem of the absence of global periodic solutions of a nonlinear Schrödinger-type evolution equation with a damped linear term. We prove that in the case where the damping factor is negative, the problem has no global periodic solutions for any initial data, and in the case of a negative damping factor, this is also true for large enough values of the initial data.

中文翻译：

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关于薛定谔型非线性演化方程的全局周期解的缺失

摘要

我们研究具有阻尼线性项的非线性薛定谔型演化方程的全局周期解不存在的问题。我们证明，在阻尼因子为负的情况下，问题对于任何初始数据都没有全局周期解，而在阻尼因子为负的情况下，对于足够大的初始数据值也是如此。