ON THE INSTABILITY OF GROUND STATES FOR A GENERALIZED DAVEY-STEWARTSON SYSTEM

doi:10.1007/s10473-020-0414-0

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (4): 1081-1090.doi: 10.1007/s10473-020-0414-0

ON THE INSTABILITY OF GROUND STATES FOR A GENERALIZED DAVEY-STEWARTSON SYSTEM

邓圆平, 李晓光, 沈倩

School of Mathematics and V. C. V. R Key Lab, Sichuan Normal University, Chengdu 610068, China

收稿日期:2019-03-15 修回日期:2020-01-07 出版日期:2020-08-25 发布日期:2020-08-21
通讯作者: Xiaoguan LI E-mail:lixgmath@163.com
作者简介:Yuanping DENG,E-mail:dengypoo@sina.com;Qian SHENG,E-mail:qiqnqsl@sina.com
基金资助:
This work was supported by the National Natural Science Foundation of China (11771314).

ON THE INSTABILITY OF GROUND STATES FOR A GENERALIZED DAVEY-STEWARTSON SYSTEM

Yuanping DENG, Xiaoguan LI, Qian SHENG

School of Mathematics and V. C. V. R Key Lab, Sichuan Normal University, Chengdu 610068, China

Received:2019-03-15 Revised:2020-01-07 Online:2020-08-25 Published:2020-08-21
Contact: Xiaoguan LI E-mail:lixgmath@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (11771314).

摘要/Abstract

摘要： 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.

关键词: Ohta's theorems, Storng instability, Davey-Stewartson system, Standing waves

Abstract: 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.

Key words: Ohta's theorems, Storng instability, Davey-Stewartson system, Standing waves

中图分类号:

35J10

邓圆平, 李晓光, 沈倩. ON THE INSTABILITY OF GROUND STATES FOR A GENERALIZED DAVEY-STEWARTSON SYSTEM[J]. 数学物理学报(英文版), 2020, 40(4): 1081-1090.

Yuanping DENG, Xiaoguan LI, Qian SHENG. ON THE INSTABILITY OF GROUND STATES FOR A GENERALIZED DAVEY-STEWARTSON SYSTEM[J]. Acta mathematica scientia,Series B, 2020, 40(4): 1081-1090.

参考文献

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[9] Li Y, Guo B L. Existence and decay of weak solutions to degenerate Davey-Stewartson equaitons. Acta Math Sci, 2002, 22B(3):302-310
[10] Ohta M. Stability of standing waves for the generalized Davey-Stewartson system. J Dyn Differ Eqs, 1994, 6:325-334
[11] Ohta M. Instability of standing waves for the generalized Davey-Stewartson system. Ann Inst Henri Poincaré, 1995, 62:69-80
[12] Ohta M. Blow-up solutions and strong instability of standing waves for the generalized Davey-Stewartson system in $\mathbb{R}^2$. Ann Inst Henri Poincare, 1995, 63:111-117
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ON THE INSTABILITY OF GROUND STATES FOR A GENERALIZED DAVEY-STEWARTSON SYSTEM

ON THE INSTABILITY OF GROUND STATES FOR A GENERALIZED DAVEY-STEWARTSON SYSTEM

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