Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shell
✍ Scribed by Nguyen Xuan Tan
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 855 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
Abstract
The purpose of this paper is to study bifurcation points of the equation T(v) = L(λ,v) + M(λ,v), (λ,v) ϵ Λ × D in Banach spaces, where for any fixed λ ϵ Λ, T, L(λ,·) are linear mappings and M(λ,·) is a nonlinear mapping of higher order, M(λ,0) = 0 for all λ ϵ Λ. We assume that λ is a characteristic value of the pair (T, L) such that the mapping T – L(λ,·) is Fredholm with nullity p and index s, p > s ⩾ 0. We shall find some sufficient conditions to show that (λ,0) is a bifurcation point of the above equation. The results obtained will be used to consider bifurcation points of the axisymmetric buckling of a thin spherical shell subjected to a uniform compressive force consisting of a pair of coupled non‐linear ordinary differential equations of second order.