| Abstract: |
| We study the instability of standing wave solutions $e^{i \omega t} \phi_{\omega}(x)$ for some nonlinear Schr\"{o}dinger equations (NLS) with or without potentials, where $\omega$ is a real parameter, and $\phi_{\omega}$ is a ground state of the corresponding stationary problem. We first review some results on strong instability by blowup of standing wave solutions for NLS with double power nonlinearity (M. Ohta and T. Yamaguchi, SUT J. Math. 51 (2015), 49--58), for NLS with an attractive delta function potential in one space dimension (M. Ohta and T. Yamaguchi, RIMS Kokyuroku Bessatsu B56 (2016), 79--92), and for NLS with a harmonic potential (M. Ohta, Funkcial. Ekvac. 61 (2018), 135--143). Then, we introduce our recent developments in this direction. |
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