Fractional Schrodinger equation; solvability and connection with classical Schrodinger equation

被引：17

作者：

Bezerra, Flank D. M. ^{[1
,2
]}

Carvalho, Alexandre N. ^{[3
]}

Dlotko, Tomasz ^{[4
]}

Nascimento, Marcelo J. D. ^{[5
]}

机构：

[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP, Brazil

[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

[3] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP, Brazil

[4] Polish Acad Sci, Inst Math, Sniadeckich 8, PL-00656 Warsaw, Poland

[5] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 457卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Fractional Schrodinger equation; Subcritical nonlinearity; Fractional powers of operators; GLOBAL ATTRACTOR; CAUCHY-PROBLEM; POWERS;

D O I：

10.1016/j.jmaa.2017.08.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Dirichlet boundary problem for semilinear fractional Schrodinger equation with subcritical nonlinear term. Local and global in time solvability and regularity properties of solutions are discussed. But our main task is to describe the connections of the fractional equation with the classical nonlinear Schrodinger equation, including convergence of the linear semigroups and continuity of the nonlinear semigroups when the fractional exponent a approaches 1. (c) 2017 Elsevier Inc. All rights reserved.

引用

页码：336 / 360

页数：25

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