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Nonsmooth Bifurcation Problems in Finite Dimensional Spaces Via Scaling of Variables

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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.

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Authors and Affiliations

  1. Department of Mathematics, Voronezh State University, 394006, Voronezh, Russia

    Mikhail Kamenskii & Boris Mikhaylenko

  2. Dipartimento di Ingegneria dell’Informazione, Università di Siena, 53100, Siena, Italy

    Paolo Nistri

Authors
  1. Mikhail Kamenskii
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  2. Boris Mikhaylenko
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  3. Paolo Nistri
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Correspondence to Paolo Nistri.

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Kamenskii, M., Mikhaylenko, B. & Nistri, P. Nonsmooth Bifurcation Problems in Finite Dimensional Spaces Via Scaling of Variables. Differ Equ Dyn Syst 20, 191–205 (2012). https://doi.org/10.1007/s12591-011-0102-6

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  • DOI: https://doi.org/10.1007/s12591-011-0102-6

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