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 -