In this paper, we give a simpler proof for Ohta’s theorems [1995, Ann. Inst. Henri Poincare, 63, 111; 1995, Diff. Integral Eq., 8, 1775] on the strong instability of the ground states for a generalized Davey-Stewartson system. In addition, a sufficient condition is given to ensure the nonexistence of a minimizer for a variational problem, which is related to the stability of the standing waves of the Davey-Stewartson system. This result shows that the stability result of Ohta [Diff. Integral Eq., 8, 1775] is sharp.

中文翻译：

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关于广义 Davey-Stewartson 系统的基态不稳定性

在本文中，我们对 Ohta 定理 [1995, Ann. 研究所 亨利庞加莱，63 岁，111 岁；1995 年，差异。Integral Eq., 8, 1775] 关于广义 Davey-Stewartson 系统基态的强不稳定性。此外，给出了一个充分条件来保证变分问题不存在极小值，这与Davey-Stewartson系统驻波的稳定性有关。该结果表明 Ohta [Diff. Integral Eq., 8, 1775] 是尖锐的。