Displaying similar documents to “Path formulation for multiparameter 𝔻 3 -equivariant bifurcation problems”

Logarithmic structure of the generalized bifurcation set

S. Janeczko (1996)

Annales Polonici Mathematici

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Let G : ℂ n × ℂ r → ℂ be a holomorphic family of functions. If Λ ⊂ ℂ n × ℂ r , π r : ℂ n × ℂ r → ℂ r is an analytic variety then    Q Λ ( G ) = ( x , u ) ∈ ℂ n × ℂ r : G ( · , u ) h a s a c r i t i c a l p o i n t i n Λ ∩ π r - 1 ( u ) is a natural generalization of the bifurcation variety of G. We investigate the local structure of Q Λ ( G ) for locally trivial deformations of Λ ₀ = π r - 1 ( 0 ) . In particular, we construct an algorithm for determining logarithmic stratifications provided G is versal.

Nonlinear eigenvalue problems for fourth order ordinary differential equations

Jolanta Przybycin (1995)

Annales Polonici Mathematici

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This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation...