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Currently displaying 1 – 4 of 4

Order by Relevance | Title | Year of publication

Zur Parameterabhängigkeit bei Differentialgleichungen.

Friedrich Schäfke; Reinhard Schäfke — 1985

Journal für die reine und angewandte Mathematik

Overstability and resonance

Augustin Fruchard; Reinhard Schäfke — 2003

Annales de l’institut Fourier

We consider a singularity perturbed nonlinear differential equation $ε u^{'} = f (x) u + + ε P (x, u, ε)$ which we suppose real analytic for $x$ near some interval $[a, b]$ and small $| u |$ , $| ε |$ . We furthermore suppose that 0 is a turning point, namely that $x f (x)$ is positive if $x \neq 0$ . We prove that the existence of nicely behaved (as $ϵ \to 0$ ) local (at $x = 0$ ) or global, real analytic or $C^{\infty}$ solutions is equivalent to the existence of a formal series solution $\sum u_{n} (x) ε^{n}$ with $u_{n}$ analytic at $x = 0$ . The main tool of a proof is a new “principle of analytic continuation” for such “overstable” solutions....

Divergence and summability of normal forms of systems of differential equations with nilpotent linear part

Mireille Canalis-Durand; Reinhard Schäfke — 2004

Annales de la Faculté des sciences de Toulouse : Mathématiques

Solutions surstables des équations différentielles complexes lentes-rapides à point tournant

Éric Benoît; Augustin Fruchard; Reinhard Schäfke; Guy Wallet — 1998

Annales de la Faculté des sciences de Toulouse : Mathématiques

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