非线性方程相对于曲线的分歧点的存在性

Existence of Bifurcation Point for Nonlinear Equation with Respect to the Curve

中文关键词:  非线性方程  Fredholm算子  隐函数定理  分歧点

英文关键词:nonlinear equation  Fredholm operator  implicit function theorem  bifurcation point.

中文摘要:

      给出了ｈ（０）为非线性方程Ｇ（ｈ）＝０相对于曲线Ｃ＝｛ｈ（λ）｜ｈ：Δ_０→Ｈ｝的分歧点的一个充分条件，推广和改进了［１—２］中的有关结果．

英文摘要:

      In this paper , we give a sufficient condition under which h (0) is a bifurcation point for nonlinear equation G(h ) = 0 with respect to the curve C = {h (λ) |Δ_０→H}. Some previousresults are extended and disproved.