非单特征值引出的非线性方程分歧问题

BIFURCATION PROBLEMS OF NONLINEAR OPERATOR EQUATIONS FROM NON-SIMPLE EIGENVALUES

本文讨论非线性方程f(x,λ)=θ的分歧问题,这里f:x×R→Y为非线性可微映射, x,Y为Banaclh空间.利用偏导算子A=fx(x0,λ0)的广义逆A+,研究了一类由非单特征值引出的分歧问题,给出了刻划分歧性的定理,推广了Crandall M G与Robinowitz P H的由单特征值引出的分歧性定理.

In this paper,we discuss the bifurcation problem in solving nonlinear operator equation f(x,λ) =0, where f is a differentiable mapping from ×R→Yand X,Y are Banach spaces.By means of the generalized inverse A+ of the partial derivatire operator A = fx(x0, λ0), a class of bifucation problems from non-simple eigenvalue has been investigaed, and we obtain a bifurcation theorem on the degenerate solutions, which extend a bifuration theorem from simple eigenvalue by Crandall and Robinowitz.