Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (4): 1081-1090.doi: 10.1007/s10473-020-0414-0

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

Yuanping DENG, Xiaoguan LI, Qian SHENG   

  1. 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).

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

CLC Number: 

  • 35J10
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