@article{Li2022, 
author = {Xiaoguang Li and Chaohe Zhang},
title = {Instability of standing waves for a quasi-linear Schrödinger equation in the critical case},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {9683-9693},
keywords = {quasi-linear Schrödinger equation, ground states, instability},
url = {https://www.sciopen.com/article/10.3934/math.2022539},
doi = {10.3934/math.2022539},
abstract = {We consider the following quasi-linear Schrödinger equation.                             i                              ∂            ψ                                ∂            t                          +        △        ψ        +        ψ        △                  |                ψ                              |                    2                +                  |                ψ                              |                                p            −            1                          ψ        =        0        ,        x        ∈                              R                    D                ,        D        ≥        1        ,                                                                                (        Q        )            where    ψ  :            R        +    ×            R        D    →      C   is the wave function,    p  =  3  +      4    D  . It is known that the set of standing waves is stable for    1  <  p  <  3  +      4    D   and it is strongly unstable for    3  +      4    D    <  p  <            3      D      +      2              D      −      2      . In this paper, we prove that the standing waves are strongly unstable for    p  =  3  +      4    D  . Moreover, a property on the set of the ground states of (Q) is investigated.}
}