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Bifurcation Theory

In: Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Author

Listed:
  • Dumitru Motreanu

    (University of Perpignan, Department of Mathematics)

  • Viorica Venera Motreanu

    (Ben-Gurion University of the Negev, Department of Mathematics)

  • Nikolaos Papageorgiou

    (National Technical University, Department of Mathematics)

Abstract

This chapter examines the bifurcation points of parametric equations, that is, values of a parameter from which the set of solutions splits into several branches. The deep connection between bifurcation points and the spectrum of linear operators involved in problems is pointed out. The presentation consists of two parts regarding the used approach: degree theory and implicit function theorem. In the latter, the theory of Fredholm operators is utilized in conjunction with the Lyapunov–Schmidt reduction method. Applications to ordinary differential equations are given. The proofs of the results presented in the chapter are complete, and novel ideas are incorporated. The basic references are mentioned in a remarks section.

Suggested Citation

  • Dumitru Motreanu & Viorica Venera Motreanu & Nikolaos Papageorgiou, 2014. "Bifurcation Theory," Springer Books, in: Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, edition 127, chapter 0, pages 181-200, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-9323-5_7
    DOI: 10.1007/978-1-4614-9323-5_7
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