Periodic Solutions for a Class of Nonlinear Partial Differential Equations in Higher Dimension

被引：25

作者：

Gentile, Guido ^{[1
]}

Procesi, Michela ^{[2
]}

机构：

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

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

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2009年 / 289卷 / 03期

基金：

欧洲研究理事会;

关键词：

WAVE-EQUATIONS; SCHRODINGER-EQUATION; CANTOR FAMILIES; KAM TORI; BOUNDARY-CONDITIONS; CONSTRUCTION; 1D; 2D;

D O I：

10.1007/s00220-009-0817-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schrodinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our result covers cases of completely resonant equations, where the bifurcation equation is infinite-dimensional, such as the nonlinear Schrodinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.

引用

页码：863 / 906

页数：44

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