Global existence, blowup phenomena, and asymptotic behavior for quasilinear Schrödinger equations

Xiaowei An, Xianfa Song

In this paper, we study the Cauchy problem of the quasilinear Schrödinger equation \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu+2uh'(|u|^2)Δh(|u|^2)+F(|u|^2)u \quad {\rm…