Bifurcation Analysis of a Class of Parametrized Two-Point Boundary Value Problems

In this paper, we study the solution eld 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 1] and Troger, Steindl 24]. The boundary value problems are formulated as an abstract operator equation T (x;) = 0 in appropriate Banach spaces of diierentiable functions. By exploiting the equivariance of T we obtain detailed informations about the structure of M. Moreover, we show how these theoretical results can be used to compute eeciently interesting parts of M with numerical standard techniques. Finally, a bifurcation diagram for the shell equations in 24] is given.