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

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Gentile, Guido
Procesi, Michela
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Abstract
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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 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.
Comment: 34 pages
Keywords
Mathematics - Analysis of PDEs, Mathematics - Dynamical Systems, 35Q55 (Primary), 37K50 (Secondary)
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