Applications of the Euler characteristic in bifurcation theory (Q1182646)

There are given sufficient conditions in terms of Brouwer degree for the existence of bifurcation points of the equation \(f(x,\lambda)=0\) in the case of a \(C^ 1\) map \(f: \mathbb{R}^ n\times\mathbb{R}^ k\to\mathbb{R}^ n\) which is homogeneous or even in an appropriate sense. These results are applied to boundary value problems of ordinary differential equations. One indicates the use of a computer program to verify the assumptions.