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 -