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Deng, Yuanping; Li, Xiaoguan; Sheng, Qian

On the instability of ground states for a generalized Davey-Stewartson system. (English) Zbl 1499.35552

Acta Math. Sci., Ser. B, Engl. Ed. 40, No. 4, 1081-1090 (2020).
Summary: In this paper, we give a simpler proof for Ohta’s theorems [M. Ohta, Differ. Integral Equ. 8, No. 7, 1775–1788 (1995; Zbl 0827.35122)] 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 [loc. cit.] is sharp.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B35 Stability in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
35J20 Variational methods for second-order elliptic equations
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian

Keywords:

Ohta’s theorems; strong instability; Davey-Stewartson system; standing waves

Citations:

Zbl 0827.35122
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\textit{Y. Deng} et al., Acta Math. Sci., Ser. B, Engl. Ed. 40, No. 4, 1081--1090 (2020; Zbl 1499.35552)
Full Text: DOI

References:

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