Applications of Generic Bifurcation. I.

摘要

In this paper, the authors give a constructive method for discussing all solutions of S(x, lambda, mu) = 0 in a neighborhood of dim (lambda sub 0, 0) for the case when S(x, lambda, mu) = I - lambda b = mu C and dim ker (I-lambda (sub 0) B'(0)) = 1 = dim co ker ((I-lambda (sub 0) B'(0)). The operators B,C may also depend on lambda, mu. The approach uses the method Liapunov-Schmidt together with some elementary ideas from catastrophe theory.