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Borel summability of divergent solutions for singular first-order partial differential equations with variable coefficients. II. (English) Zbl 1147.35017
Summary: Under a certain restriction, singular first-order linear partial differential equations of nilpotent type with two variables are divided into two classes. In Part I [J. Differ. Equations 227, No. 2, 499–533 (2006; Zbl 1147.35016)], we dealt with the one class, and comprehended that there was a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients. In this second part, we give a similar consideration on the other class. More precise global estimates than those given in Part I for coefficients will be required to prove the Borel summability of divergent solutions.

MSC:
35C20 Asymptotic expansions of solutions to PDEs
35C10 Series solutions to PDEs
35C15 Integral representations of solutions to PDEs
35F05 Linear first-order PDEs
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[1] Hibino, M., Borel summability of divergent solutions for singular first order linear partial differential equations with polynomial coefficients, J. math. sci. univ. Tokyo, 10, 279-309, (2003) · Zbl 1036.35051
[2] M. Hibino, Borel summability of divergent solutions for singular first order linear partial differential equations with variable coefficients. Part I, preprint · Zbl 1147.35017
[3] M. Hibino, Borel summability of divergent solutions for singularly perturbed first-order ordinary differential equations, Tohoku Math. J. (2), in press · Zbl 1118.34083
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