Some Applications of Degree Theory to Bifurcation Problems

Abstract

Some results on the vanishing of a generalized degree of multivalued mappings are proved and applied to study bifurcation solutions of the equation $F(\lambda ,u)=0$ in a Banach space; as a special case, $F(\lambda ,u)=u—M(u)—N(\lambda ,u)—H(\lambda ,u)$, where the parameter $\lambda$ is from a normed space. For concrete application there are considered bifurcation solutions of a nonlinear elliptic differential equation of second order.