Surstabilité pour une équation différentielle analytique en dimension un. (Overstability for an analytic differential equation in dimension one)
With regard to the delayed bifurcation problem, the notion of overstable solution is defined for a family of analytic differential equation with a small parameter. With the help of nonstandard asymptotic analysis, we prove that overstable solutions exist for some exceptional values of a control parameter. The main tool of the demonstration is a summation theorem which constitutes a generalization of a A. N. Neishtadt's result.
analytic differential equation with a small parameter
scientific article; zbMATH DE number 4138217
scientific article