Geodesic
A Local Hopf Bifurcation Theorem for a Certain Class of Implicit Differential Equations
Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 183-189

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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.
DOI : 10.4153/CMB-1993-027-0
Mots-clés : 34A09, 34C23, 47H15, 58E09 
Kaczynski, Tomasz; Krawcewicz, Wieslaw. A Local Hopf Bifurcation Theorem for a Certain Class of Implicit Differential Equations. Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 183-189. doi: 10.4153/CMB-1993-027-0
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     title = {A {Local} {Hopf} {Bifurcation} {Theorem} for a {Certain} {Class} of {Implicit} {Differential} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {183--189},
     year = {1993},
     volume = {36},
     number = {2},
     doi = {10.4153/CMB-1993-027-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-027-0/}
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