{"product_id":"equivariant-lyapunof-center-theorem-von-cristina-bardelle","title":"Equivariant Lyapunof Center Theorem","description":"\u003cp\u003eWe 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783843354004\"\u003e\u003ch3\u003efor Partial Differential Equations\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783843354004","offer_id":39497118842973,"sku":"9783843354004","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/732f5594-3d96-466f-aa1a-be58c57d29bd.jpg?v=1757741518","url":"https:\/\/shop.autorenwelt.de\/products\/equivariant-lyapunof-center-theorem-von-cristina-bardelle","provider":"Autorenwelt Shop","version":"1.0","type":"link"}