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A fold bifurcation theorem of degenerate solutions in a perturbed nonlinear equation. (English) Zbl 1230.37060

Consider a nonlinear equation \(F(\varepsilon,\lambda,u)=0\), where \(\varepsilon\) is a perturbation parameter, \(\lambda\) is a real number, \(u\) belongs to a Banach space, and \(F\) is a differentiable mapping into a Banach space. The authors use the generalized saddle-node bifurcation theorem to obtain a general bifurcation result.

MSC:

37G10 Bifurcations of singular points in dynamical systems
37H20 Bifurcation theory for random and stochastic dynamical systems
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