Equivariant Lyapunof Center Theorem

Equivariant Lyapunof Center Theorem

for Partial Differential Equations

LAP Lambert Academic Publishing ( 21.09.2010 )

€ 49,00

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We prove the existence of small amplitude quasi- periodic solutions of some nonlinear Hamiltonian partial differential equations, exploiting the symmetries of the systems. Our theorem is obtained requiring a Dyophantine type nonresonance condition, a standard nondegeneracy condition and assuming a regularizing property of the nonlinearity. The proof is based on the Lyapunov-Schmidt reduction method, a suitable analysis of small denominators and on the standard implicit function theorem. We apply our result to the nonlinear beam equation with spatial periodic boundary conditions, to a beam vibrating in a two dimensional space with Dirichlet boundary conditions and to the nonlinear wave equation with spatial periodic boundary conditions.

Kitap detayları:

ISBN-13:

978-3-8433-5400-4

ISBN-10:

3843354006

EAN:

9783843354004

Kitabın dili:

English

Yazar:

Cristina Bardelle

Sayfa sayısı:

84

Yayın tarihi:

21.09.2010

Kategori:

Matematik