Wellposedness for semirelativistic Schrodinger equation with power-type nonlinearity

被引：23
|
作者：
Shi, Qihong [1 ]
Peng, Congming [2 ]
机构：
[1] Lanzhou Univ Technol, Dept Math, Lanzhou 730000, Gansu, Peoples R China
[2] Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 178卷
基金：
中国国家自然科学基金;
关键词：
Semirelativistic equation; Cubic nonlinearity; Low regularity; Wellposedness; WELL-POSEDNESS; CAUCHY-PROBLEM; REGULARITY; SPACE;
D O I：
10.1016/j.na.2018.07.012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we employ Bourgain type norm to investigate the wellposedness for the Cauchy problem of one dimensional semirelativistic Schrodinger equation with cubic nonlinearity in space H-s. We extend the previous existence result to the space regularity s >= 1/4. Moreover, we point out the persistence of the solution in different regularity space is uniform by an iterate argument. Additionally, we are also able to say more for semirelativistic Schrodinger equation with general power-type nonlinearity. (C) 2018 Elsevier Ltd. All rights reserved.
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页码：133 / 144
页数：12
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