Formal and convergent power series solutions of singular partial differential equations
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- by Stanley Kaplan PDF
- Trans. Amer. Math. Soc. 256 (1979), 163-183 Request permission
Abstract:
A class of singular first-order partial differential equations is described for which an analogue of a theorem of M. Artin on the solutions of analytic equations holds: given any formal power series solution and any nonnegative integer v, a convergent power series solution may be found which agrees with the given formal solution up to all terms of order $\leqslant v$.References
- M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277–291. MR 232018, DOI 10.1007/BF01389777
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745 F. R. Gantmacher, The theory of matrices. Vol. 2, Chelsea, New York. E. Goursat, Leçons sur l’intégration des équations aux dérivées partielles du premier ordre, A. Hermann, Librairie Scientifique, Paris, 1891. H. Poincaré, Sur les propriétés des fonctions définies par les équations aux différences partielles, Oeuvres, Tome 1. Gauthier-Villars, Paris, 1951.
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 256 (1979), 163-183
- MSC: Primary 35C10; Secondary 14B12, 32B05, 35A35
- DOI: https://doi.org/10.1090/S0002-9947-1979-0546913-5
- MathSciNet review: 546913