Ukrainian Mathematical Journal

, Volume 42, Issue 3, pp 350–354 | Cite as

Analyticity with respect to a parameter of regular solutions of weakly nonlinear singularly perturbed problems

  • V. F. Safonov
Brief Communications


We consider a weakly nonlinear singular perturbed problem with right side independent of time. We show that the regularized asymptotic series obtained by Lomov's method are analytic with respect to the parameter and regularizing variables.


Regular Solution Asymptotic Series 
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Literature cited

  1. 1.
    Yu. P. Gubin and V. F. Safonov, “Asymptotic solutions of singularly perturbed problems with weak nonlinearity in the case of nonidentical resonance,” Differents. Uravn.,20, No. 6, 930–941 (1984).Google Scholar
  2. 2.
    S. A. Lomov, Introduction to the General Theory of Singular Perturbations [in Russian], Nauka, Moscow (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • V. F. Safonov
    • 1
  1. 1.Moscow Energy InstituteUSSR

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