Electron. J. Differential Equations, Vol. 2020 (2020), No. 27, pp. 1-14.

Global asymptotic behavior of solutions to quasilinear schrodinger equations

Lin Zhang, Xianfa Song

Abstract:
We are concerned with the existence and blowup of solutions for a class of quasilinear Schrodinger equations. In particular, we examine the combined effect of local type nonlinearity and Hartree type ones, and depending upon different parameter regimes, we find the dominant roles exhibited by these nonlinear effects. We also consider the asymptotic behavior for the global solution and lower bound for the blowup rate of the blowup solution by using pseudo-conformal conservation laws.

Submitted October 24, 2019 Published March 31, 2020.
Math Subject Classifications: 35B44, 35Q55.
Key Words: Qusilinear Schrodinger equation; global solution; blow up; asymptotic behavior.
DOI: 10.58997/ejde.2020.27

Show me the PDF file (310 KB), TEX file for this article.

Lin Zhang
Center of Applied Mathematics
School of Mathematics, Tianjin University
Tianjin, 300072, China
email: LinZhangYH@163.com
Xianfa Song
Department of Mathematics
School of Mathematics, Tianjin University
Tianjin, 300072, China
email: songxianfa@tju.edu.cn

Return to the EJDE web page