Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shell

Abstract

The purpose of this paper is to study bifurcation points of the equation

in Banach spaces, where for any fixed λ ∈ T, L(λ,·) are linear mappings and M(λ,·) is a nonlinear mapping of higher order, M(λ, 0) = 0 for all λ ∈ Λ. We assume that is a characteristic value of the pair (T, L) such that the mapping is Fredholm with nullity p and index .s, p> s ≥ 0. We shall find some sufficient conditions to show that is a bifurcation point of the above equation. The obtained results will be applied 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 nonlinear ordinary differential equations of second order.

Keywords:

• Characteristic value
• Fredholm operator
• bifurcation
• nonlinear operators
• nonlinear ordinary differential equations

AMS:

• 34G20
• 58F10
• 47H15