Functional Analysis and Its Applications

, Volume 39, Issue 3, pp 215–224 | Cite as

On the Convergence of Formal Solutions of a System of Partial Differential Equations

  • S. P. Chulkov


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.”

Key words

systems of partial differential equations convergence of formal solutions ordered semigroup ℤ⩾0n system of partial differential equations solved for the highest-order derivatives system of partial differential equations “almost solved for the highest-order derivatives” 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. P. Chulkov
    • 1
    • 2
  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Independent University of MoscowMoscowRussia

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