**Preprint series:**
99-09, Reports on Numerical Mathematics

**The paper is published:**
Technische Mechanik, Band 19, Heft 1, (1999),

**MSC:**- 65L10 Boundary value problems
- 65J15 Equations with nonlinear operators (do not use 65Hxx)
- 73H05 Buckling
- 73K15 Shells

**Abstract:** Abstract:

We study the solution field M of a parameter dependent nonlinear two-point

boundary value problem suggested by Bauer et al. 1970. This problem describes

the buckling of a thin-walled spherical shell under a uniform axisymmetric

external static pressure. The boundary value problem is 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. In Part II of this work, the theoretical results are used to

efficiently compute interesting parts of M with numerical standard

techniques.

**Upload:** 1999-02-24

**Update:** 1999-03-03

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