Sibuya, Yasutaka 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 Cited in 1 ReviewCited in 4 Documents MSC: 34E05 Asymptotic expansions of solutions to ordinary differential equations Keywords:holomorphic coefficients; formal solution; Gevrey order Citations:Zbl 0689.00009 PDFBibTeX XML