, Volume 20, Issue 3, pp 191-205

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.