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Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shell
Author(s) -
Tan Nguyen Xuan
Publication year - 1993
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670160103
Subject(s) - mathematics , bifurcation , bifurcation theory , multiplicity (mathematics) , mathematical analysis , buckling , rotational symmetry , ordinary differential equation , shell (structure) , nonlinear system , partial differential equation , differential equation , geometry , physics , materials science , composite material , quantum mechanics , thermodynamics
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.