Persistence and bifurcation of degenerate solutions (Q1969453)

The author studies an equation \(F(\varepsilon,\lambda,u)=0\), where \(F:{\mathbb R}\times {\mathbb R}\times X\rightarrow Y\) is a smooth nonlinear map and \(X, Y\) are Banach spaces. It is obtained a number of bifurcation results for degenerate solutions. Several applications to elliptic boundary value problems of the form \(Lu+\lambda f(\varepsilon, u)=0\) are presented.