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Bifurcation

In: Nonlinear Functional Analysis

Author

Listed:
  • Klaus Deimling

    (Gesamthochschule Paderborn)

Abstract

In this last chapter we shall indicate how degree theory, implicit function theorems and variational methods can be used in the study of the solution set S of an equation F(λ, x) = 0, where the splitting of the independent variable into λ ∈ Λ and x ∈X is motivated by concrete models in which the λ are considered as parameters. The latter means that the λ ∈ Λ are those independent variables, say of technical significance, which the practical man wants to manipulate. So, he is interested in the slices S(λ) = {x ∈ X:(λ, x)∈S} and especially in the parameters λ0 at which the S(λ) change their structure.

Suggested Citation

  • Klaus Deimling, 1985. "Bifurcation," Springer Books, in: Nonlinear Functional Analysis, chapter 0, pages 378-425, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-00547-7_10
    DOI: 10.1007/978-3-662-00547-7_10
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