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

Gentile, G., Procesi, M. (2009). Periodic solutions for a class of nonlinear partial differential equations in higher dimension. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 289(3), 863-906 [10.1007/s00220-009-0817-1].

Periodic solutions for a class of nonlinear partial differential equations in higher dimension

GENTILE, Guido;PROCESI, MICHELA
2009-01-01

Abstract

We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger 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 Schroedinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.
Gentile, G., Procesi, M. (2009). Periodic solutions for a class of nonlinear partial differential equations in higher dimension. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 289(3), 863-906 [10.1007/s00220-009-0817-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/141581
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