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March 2017 Generalized Poincaré Condition and Convergence of Formal Solutions of Some Nonlinear Totally Characteristic Equations
Hidetoshi TAHARA
Tokyo J. Math. 39(3): 863-883 (March 2017). DOI: 10.3836/tjm/1475723091

Abstract

This paper discusses a holomorphic nonlinear singular partial differential equation $(t \partial_t)^mu=F(t,x,\{(t \partial_t)^j \partial_x^{\alpha}u \}_{j+\alpha \leq m, j<m})$ that is of nonlinear totally characteristic type. The Newton Polygon at $x=0$ of the equation is defined, and by means of this polygon we define a generalized Poincaré condition (GP) and a condition (R) that the equation has a regular singularity at $x=0$. Under these conditions, (GP) and (R), it is proved that every formal power series solution is convergent in a neighborhood of the origin.

Citation

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Hidetoshi TAHARA. "Generalized Poincaré Condition and Convergence of Formal Solutions of Some Nonlinear Totally Characteristic Equations." Tokyo J. Math. 39 (3) 863 - 883, March 2017. https://doi.org/10.3836/tjm/1475723091

Information

Published: March 2017
First available in Project Euclid: 6 October 2016

zbMATH: 1373.35081
MathSciNet: MR3634296
Digital Object Identifier: 10.3836/tjm/1475723091

Subjects:
Primary: 35A20
Secondary: 35A01, 35C10

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.39 • No. 3 • March 2017
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