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math.AP2018
A quasilinear Schrödinger equation with Hartree type nonlinearity
Xianfa Song, Zhi-Qiang Wang
In this paper, we deal with the Cauchy problem of the quasilinear Schödinger equation \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu+2uh'(|u|^2)Δh(|u|^2)+(W(x)\ast|u|^2)u,\ x…
math.AP2018★ 1 cited
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 fo…