Cantor families of periodic solutions for completely resonant nonlinear wave equations

Details Cantor families of periodic solutions for completely resonant nonlinear wave equations Cantor families of periodic solutions for completely resonant nonlinear wave equations

2004-10-29

arxiv.org/abs/math/0410618v1

Mathematics

Analysis of PDEs

Scientific paper

We prove existence of small amplitude, $2\pi \slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.

Affiliated with

Also associated with

No associations

Rating

Cantor families of periodic solutions for completely resonant nonlinear wave equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cantor families of periodic solutions for completely resonant nonlinear wave equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cantor families of periodic solutions for completely resonant nonlinear wave equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-479948