Bifurcation analysis of a class of parametrized two-point boundary value problems

摘要

In this paper, we study the solution manifold M of a class of nonlinear parametrized two-point boundary value problems. Typical representatives of this class are the shell equations of Bauer, Reiss, Keller [2] and Troger, Steindl [29]. The boundary value problems are formulated as an abstract operator equation T(x, lambda) = 0 in appropriate Banach spaces. By exploiting the equivariance of T, we obtain detailed information about the structure of M. Moreover, we show how these theoretical results can be used to compute efficiently interesting parts of M with numerical standard techniques. Finally, we present numerical results for the shell equations given in [2] and [29]. [References: 30]