Analysis of a bifurcation problem (Q1349167)

A bifurcation problem of the type \(u-\lambda Lu+g(\lambda,u,y)=0\) in a neighborhood of a particular solution \((\lambda_0,0,0)\in \mathbb{R}\times E\times F\) is considered. Here \(E, F\) are real Banach spaces and \(\lambda_0\) is a semisimple characteristic number of the linear operator \(L\). Under certain assumptions about the perturbating nonlinearity the authors prove the existence of a bifurcation. The main results of the article consist in the application of Galerkin's method to reduce the space. Numerical results are discussed.