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

In this paper, we study the solution field M of a class of nonlinear parametrized twopoint 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 differentiable 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 efficiently interesting parts of M with numerical standard techniques. Finally, a bifurcation diagram for the shell equations in [24] is given