Ukrainian Mathematical Journal

, Volume 36, Issue 6, pp 552–555 | Cite as

Asymptotic behavior of the solution of the Dirichlet problem for a differential operator with a small parameter

  • V. V. Sarafyan
  • R. G. Safaryan


Asymptotic Behavior Differential Operator Small Parameter Dirichlet Problem 
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Literature cited

  1. 1.
    N. Levinson, “The first boundary-value problem for ɛδU+A(x, y)Ux+B(x, y)Uy + C(x, y)U=D(x, y) for small ɛ,” Ann. Math., Ser. 2,51, 428–445 (1950).Google Scholar
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    R. Z. Khas'minskii, “On the averaging principle for parabolic and elliptic differential equations and Markov processes with small diffusion,” Teor. Veroyatn. Primen.,8, No. 1, 3–25 (1963).Google Scholar
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    I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes [in Russian], Nauka, Moscow (1965).Google Scholar
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    V. V. Sarafyan, “On the asymptotic behavior of the first eigenvalue of an elliptic operator with a small parameter,” Dokl. Akad. Nauk ArmSSR,25, No. 3, 79–83 (1982).Google Scholar
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    R. G. Safaryan, “Some boundary-value problems with a small parameter for degenerate diffusion processes and the corresponding differential equations,” Izv. Akad. Nauk ArmSSR, Mat.,15, No. 4, 258–267 (1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • V. V. Sarafyan
    • 1
  • R. G. Safaryan
    • 1
  1. 1.Armenian Pedagogical InstituteUSSR

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