一个分歧定理

本文用 Morse 理论给出 Krasnoselski Rabinowitz 关于位算子分歧点定理的一个新的证明.设 H 是一个 Hilbert 空间,Ω 是 H 中零元θ的一个邻域.又设 L 是 H 上的一个有界自伴算子,而 G∈C(Ω,H)满足 G(u)=o(‖u‖),当 u→θ.倘若 G 还是一个位算子,即存在 g∈C~1(Ω,R~1),使得 dg=G.求解带参数 λ∈R~1的方程

A BIFURCATION THEOREM

A simple but completely different proof of the bifurcation theorem,which descri-bes possible behavior of the set of solutions for potential operators with a real parameter in a neighborhood of a bifurcation point,is presented.The method is based on theMorse theory of isolated critical points.A homotopy invariance theorem for critical gro-ups of isolated critical points is proved.