We prove an abstract Nash Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the tame estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on RiemannianZoll manifolds.
M., B., P., B., Procesi, M. (2010). An abstract Nash-Moser Theorem with parameters and applications to PDEs. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 27, 377-399 [10.1016/j.anihpc.2009.11.010].
An abstract Nash-Moser Theorem with parameters and applications to PDEs
PROCESI, MICHELA
2010-01-01
Abstract
We prove an abstract Nash Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the tame estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on RiemannianZoll manifolds.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
