A Local Hopf Bifurcation Theorem for a Certain Class of Implicit Differential Equations

Kaczynski, Tomasz ; Krawcewicz, Wieslaw

Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 183-189

Résumé

The local Hopf Bifurcation theorem is extended to implicit differential equations in Rn , of the form ẋ = f(x,ẋ, α), which are not solvable for the variable ẋ. The proof uses the S1 -degree of convex-valued mappings. An example of an implicit differential equation in R 3 to which the presented theorem applies is provided.

Détail

DOI : 10.4153/CMB-1993-027-0

Mots-clés : 34A09, 34C23, 47H15, 58E09

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