Periodic solutions for the Schrodinger equation with nonlocal smoothing nonlinearities in higher dimension

被引：9

作者：

Gentile, Guido ^{[1
]}

Procesi, Michela ^{[1
,2
]}

机构：

[1] Univ Roma Tre, Dipartimento Matemat, I-00146 Rome, Italy

[2] Univ Naples Federico 2, Dipartimento Matemat, I-80126 Naples, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年 / 245卷 / 11期

关键词：

D O I：

10.1016/j.jde.2008.02.037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the nonlinear Schrodinger equation in higher dimension with Dirichlet boundary conditions and with a nonlocal smoothing nonlinearity. We prove the existence of small amplitude periodic solutions. In the fully resonant case we find solutions which at leading order are wave packets, in the sense that they continue linear solutions with an arbitrarily large number of resonant modes. The main difficulty in the proof consists in a "small divisor problem" which we solve by using a renormalisation group approach. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：3253 / 3326

页数：74

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