2m阶Schrodinger方程组在实指数Sobolev空间中的整体小解

The Small Global Solution for the Coupled 2mth-order Nonlinear System on Real Index Sobolev Space

通过应用Banach不动点定理,该文研究了在任意维数空间中2 m阶非线性Schr dinger方程组i u t+(-Δ)mu=auα-1 uvβ+1,x∈Rn,t≥0,i v t+(-Δ)mv=buα+1vβ-1 v,x∈Rn,t≥0,u(x,0)=φ(x),v(x,0)=ψ(x),x∈Rn在实指数Sobolev空间H s p 1(Rn)×H s p 2(Rn)中的整体小解.

Schr?dinger type equation plays an important role in evolution equations.By using Banach fixed point theorem,the small global solutions of the following 2mth-order nonlinear Schr?dinger systemi u t+(-Δ)mu=auα-1 uvβ+1,x∈Rn,t≥0,i v t+(-Δ)mv=buα+1vβ-1 v,x∈Rn,t≥0,u(x,0)=φ(x),v(x,0)=ψ(x),x∈Rn in arbitrary dimensions are studied on the Sobolev space Hsp1(Rn)×Hsp2(Rn).