1 citations · 1 across the 7 of their papers we have counts for
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Critical line of exponents, scattering theories for a weighted gradient system of semilinear wave equations
Xianfa Song
In this paper, we consider the following Cauchy problem of a weighted gradient system of semilinear wave equations \begin{equation*} \left\{ \begin{array}{lll} u_{tt}-Δu=λ|u|^α|v|^…
The role of potential, Morawetz estimate and spacetime bound for quasilinear Schrödinger equations
Xianfa Song
In this paper, we deal with the following Cauchy problem \begin{equation*} \left\{ \begin{array}{lll} iu_t = Δu + 2uh'(|u|^2)Δh(|u|^2) + V(x)u,\ x\in \mathbb{R}^N,\ t>0\\ u(x,0) =…
Morawetz estimates and spacetime bounds for quasilinear Schrödinger equations with critical Sobolev exponent
Xianfa Song
In this paper, we study the following Cauchy problem \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu + 2uh'(|u|^2)Δh(|u|^2) + F(|u|^2)u\mp A[h(|u|^2]^{2^*-1} h'(|u|^2)u,\ x\in…
Spacetime estimates and scattering theory for quasilinear Schrödinger equations in arbitrary space dimension
Xianfa Song
In this paper, we consider the following Cauchy problem of \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu+2δ_huh'(|u|^2)Δh(|u|^2)+V(x)u+F(|u|^2)u+(W*|u|^2)u,\ x\in \mathbb{R}…