Abstract
We study a version of the classical problem on the convergence of formal solutions of systems of partial differential equations. A necessary and sufficient condition for the convergence of a given formal solution (found by any method) is proved. This convergence criterion applies to systems of partial differential equations (possibly, nonlinear) solved for the highest-order derivatives or, which is most important, “almost solved for the highest-order derivatives.”
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Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 39, No. 3, pp. 64–75, 2005
Original Russian Text Copyright © by S. P. Chulkov
Partially supported by grants RFBR-01-01-00739 and NSh-1972.2003.1.
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Chulkov, S.P. On the Convergence of Formal Solutions of a System of Partial Differential Equations. Funct Anal Its Appl 39, 215–224 (2005). https://doi.org/10.1007/s10688-005-0040-6
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DOI: https://doi.org/10.1007/s10688-005-0040-6