TY - JOUR T1 - Degenerate KAM theory for partial differential equations JF - Journal of Differential Equations Y1 - 2011 A1 - Dario Bambusi A1 - Massimiliano Berti A1 - Elena Magistrelli AB - 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. VL - 250 N1 - cited By (since 1996)3 ER - TY - JOUR T1 - A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs JF - SIAM J. Math. Anal. 37 (2006) 83-102 Y1 - 2006 A1 - Dario Bambusi A1 - Massimiliano Berti AB - 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. UR - http://hdl.handle.net/1963/2159 U1 - 2085 U2 - Mathematics U3 - Functional Analysis and Applications ER -