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Gevrey property of formal solutions in a parameter. (English) Zbl 0715.34106

Asymptotic and computational analysis. Conference in honor of Frank W.J. Olver’s 65th birthday, Proc. Int. Symp., Winnipeg/Can. 1989, Lect. Notes Pure Appl. Math. 124, 393-401 (1990).
[For the entire collection see Zbl 0689.00009.]
For the singular first order system of ODE \[ \epsilon^{\sigma}dy/dx=f(x,\epsilon)+A(x,\epsilon)+\sum_{| p| \geq 2}f_ p(x,\epsilon)y^ p \] with holomorphic coefficients the existence of a unique formal solution in the form of formal series in \(\epsilon\) of Gevrey order 1/\(\sigma\) with holomorphic and bounded coefficients is established.
Reviewer: Yu.V.Rogovchenko

MSC:

34E05 Asymptotic expansions of solutions to ordinary differential equations

Citations:

Zbl 0689.00009