[1]王海龙,郭翠花*.2m阶Schrdinger方程组在实指数Sobolev 空间中的整体小解[J].江西师范大学学报(自然科学版),2020,(03):263-268.[doi:10.16357/j.cnki.issn1000-5862.2020.03.09]
　WANG Hailong,GUO Cuihua*.The Small Global Solution for the Coupled 2mth-order Nonlinear System on Real Index Sobolev Space[J].Journal of Jiangxi Normal University:Natural Science Edition,2020,(03):263-268.[doi:10.16357/j.cnki.issn1000-5862.2020.03.09]
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2m阶Schrödinger方程组在实指数Sobolev 空间中的整体小解()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2020年03期
页码:
263-268
栏目:
数学与应用数学
出版日期:
2020-06-10

文章信息/Info

Title:
The Small Global Solution for the Coupled 2mth-order Nonlinear System on Real Index Sobolev Space
文章编号:
1000-5862(2020)03-0263-06
作者:
王海龙; 郭翠花*
山西大学数学科学学院,山西 太原 030006
Author(s):
WANG Hailong; GUO Cuihua*
School of Mathematical Sciences,Shanxi University,Taiyuan Shanxi 030006,China
关键词:
2m阶耦合Schrö; dinger方程组;  实指数Sobolev空间;  整体小解;  Banach不动点原理
Keywords:
coupled 2mth-order Schrö; dinger system;  real index Sobolev space;  small global solution;  Banach fixed point theorem
分类号:
O 175
DOI:
10.16357/j.cnki.issn1000-5862.2020.03.09
文献标志码:
A
摘要:
Schrödinger型方程是一类非常重要的发展方程.通过应用Banach不动点定理,该文研究了在任意维数空间中2m阶非线性Schrödinger方程组{iut+(-Δ)mu=a|u|α-1u|v|β+1,x∈Rn,t≥0,ivt+(-Δ)mv=b|u|α+1|v|β-1v,x∈Rn,t≥0,u(x,0)=φ(x),v(x,0)=ψ(x),x∈Rn在实指数Sobolev空间Hsp1(Rn)×Hsp2(Rn)中的整体小解.
Abstract:
Schrödinger 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 Schrödinger system{iut+(-Δ)mu=a|u|α-1u|v|β+1,x∈Rn,t≥0,ivt+(-Δ)mv=b|u|α+1|v|β-1v,x∈Rn,t≥0,u(x,0)=φ(x),v(x,0)=ψ(x),x∈Rnin arbitrary dimensions are studied on the Sobolev space Hsp1(Rn)×Hsp2(Rn).

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2019-09-10
基金项目:国家自然科学基金(61503230)资助项目.
通信作者:郭翠花(1972-),女,山西平遥人,教授,博士,主要从事非线性偏微分方程及其应用研究.E-mail:gchzjq@sxu.edu.cn
更新日期/Last Update: 2020-06-10