具有二维核空间的分支解的有限维逼近

THE FINITE DIMENSIONAL APPROXIMATION OF BIFURCATION SOLUTIONS WITH TWO DIMENSIONAL NULL SPACES

其中X_h是X的有限维子空间。[1—6]中对(1)的正常解支、单重极限点附近的解支以及简单分支点附近的解支这三种不同情形,分别讨论了逼近问题(2)的解的性质以及和(1)的解之间的误差估计。特别指出了在简单分支点附近,(2)一般不存在分支点。在工程结构的稳定性和过层曲分析中以及结构的屈曲优化设计中。

Let's consider the nonlinear equation in Banach space as follows: F(x,λ) =0(1), and itsfinite dimensional approximation equation F_h(x,λ)=0(2). Suppose that (x~*,λ~*) is a solutionof(1) and that dimKerF_x. (x~*,λ~*) =2. In this papar, some generalizations of the Morse lem-ma are proposed. Then, by using these generalized Morse lemmas, the approximation beha-viours of solution set of (2) concerning solution set of (1) are investigated.