Data di Pubblicazione:
2005
Citazione:
A Birkhoff-Lewis-Type theorem for some Hamiltonian PDEs / D. Bambusi, M. Berti. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 37:1(2005), pp. 83-102.
Abstract:
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
infinite dimensional Hamiltonian systems ; periodic solutions ; Birkhoff normal form ; variational methods ; perturbation theory
Elenco autori:
D. Bambusi, M. Berti
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