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

详细信息    查看全文

• 作者：Guido Gentile and Michela Procesi
• 刊名：Communications in Mathematical Physics
• 出版年：2009
• 出版时间：August, 2009
• 年：2009
• 卷：289
• 期：3
• 页码：863-906
• 全文大小：634.8 KB

文摘

We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schr?dinger 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 Schr?dinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.