带 Hardy 位势的非线性薛定谔方程驻波解的强不稳定性
Strong Instability of Standing Waves for the Nonlinear Schrodinger Equation with Hardy Potential
DOI: 10.12677/PM.2023.137212, PDF, 下载: 200  浏览: 273 
作者: 秦绪芬：西北师范大学数学与统计学院，甘肃 兰州
关键词: 非线性薛定谔方程；Hardy 位势；强不稳定性；驻波解；Nonlinear Schrodinger Equation； Hardy Potential； Strong Instability； Standing Waves
摘要: 本文研究了带 Hardy 位势和混合非线性项的薛定谔方程基态驻波解的强不稳定性。通过建立基态解的变分刻画，在基态解的邻域内构造了爆破解的存在性。从而证明了基态驻波解的强不稳定性。
Abstract: The aim of this paper is to study the strong instability of ground state standing waves for the Schrodinger equation with hardy potential and combined nonlinearilities. By establishing the variational characterization of the ground states, the existence of the finite time blow-up is constructed in the neighborhood of the ground state solution, and the strong instability of the ground state standing wave is proved.
文章引用：秦绪芬. 带 Hardy 位势的非线性薛定谔方程驻波解的强不稳定性[J]. 理论数学, 2023, 13(7): 2057-2068. https://doi.org/10.12677/PM.2023.137212

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