Differential Equations and Dynamical Systems

, Volume 20, Issue 3, pp 191–205

Nonsmooth Bifurcation Problems in Finite Dimensional Spaces Via Scaling of Variables

  • Mikhail Kamenskii
  • Boris Mikhaylenko
  • Paolo Nistri
Original Research

DOI: 10.1007/s12591-011-0102-6

Cite this article as:
Kamenskii, M., Mikhaylenko, B. & Nistri, P. Differ Equ Dyn Syst (2012) 20: 191. doi:10.1007/s12591-011-0102-6

Abstract

We consider a nonsmooth bifurcation equation depending on a small parameter \({\varepsilon > 0}\) . In Theorem 1 we provide conditions ensuring the existence of branches of solutions, smoothly depending on \({\varepsilon}\) , emanating from a curve of solutions of the bifurcation equation when \({\varepsilon = 0.}\) Several examples will illustrate the different types of bifurcation that occur in the present nonsmooth case.

Keywords

Nonsmooth bifurcation Branches of solutions Implicit function theorem 

Copyright information

© Foundation for Scientific Research and Technological Innovation 2012

Authors and Affiliations

  • Mikhail Kamenskii
    • 1
  • Boris Mikhaylenko
    • 1
  • Paolo Nistri
    • 2
  1. 1.Department of MathematicsVoronezh State UniversityVoronezhRussia
  2. 2.Dipartimento di Ingegneria dell’InformazioneUniversità di SienaSienaItaly

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