%0 Journal Article
%J Journal of Differential Equations
%D 2011
%T Degenerate KAM theory for partial differential equations
%A Dario Bambusi
%A Massimiliano Berti
%A Elena Magistrelli
%X This paper deals with degenerate KAM theory for lower dimensional elliptic tori of infinite dimensional Hamiltonian systems, depending on one parameter only. We assume that the linear frequencies are analytic functions of the parameter, satisfy a weak non-degeneracy condition of Rüssmann type and an asymptotic behavior. An application to nonlinear wave equations is given. © 2010 Elsevier Inc.
%B Journal of Differential Equations
%V 250
%P 3379-3397
%G eng
%R 10.1016/j.jde.2010.11.002
%0 Journal Article
%J SIAM J. Math. Anal. 37 (2006) 83-102
%D 2006
%T A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs
%A Dario Bambusi
%A Massimiliano Berti
%X In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity.
%B SIAM J. Math. Anal. 37 (2006) 83-102
%G en_US
%U http://hdl.handle.net/1963/2159
%1 2085
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T09:24:09Z\\nNo. of bitstreams: 1\\n0310182v1.pdf: 221749 bytes, checksum: 1ca47fecc44576d771b14ead5f53db0e (MD5)
%R 10.1137/S0036141003436107