Electron. J. Differential Equations, Vol. 2021 (2021), No. 39, pp. 1-18.

Blow-up criteria and instability of standing waves for the inhomogeneous fractional Schrodinger equation

Binhua Feng, Zhiqian He, Jiayin Liu

Abstract:
In this article, we study the blow-up and instability of standing waves for the inhomogeneous fractional Schrodinger equation

where $s\in (\frac{1}{2},1)$, $0<b<\min \{2s,N\}$ and $0<p< \frac{4s-2b}N-2s}$. In the L2-critical and L2-supercritical cases, i.e., $\frac{4s-2b}{N}\leq p< \frac{4s-2b}{N-2s}$, we establish general blow-up criteria for non-radial solutions by using localized virial estimates. Based on these blow-up criteria, we prove the strong instability of standing waves.

Submitted November 28, 2020. Published May 7, 2021.
Math Subject Classifications: 35B35, 35B40, 35K57, 35Q92, 92C17.
Key Words: Inhomogeneous fractional Schrodinger equation; blow-up criteria; strong instability.
DOI: https://doi.org/10.58997/ejde.2021.39

Show me the PDF file (396 KB), TEX file for this article.

Binhua Feng
Department of Mathematics
Northwest Normal University
Lanzhou,730070, China
email: binhuaf@163.com
  Zhiqian He
Department of Basic Teaching and Research
Qinghai University
Xining 810016, China
email: zhiqianhe1987@163.com
Jiayin Liu
School of Mathematics and Information Science
North Minzu University
Yinchuan 750021, China
email: xecd@163.com

Return to the EJDE web page