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Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator

Author

Listed:
  • Burkhan T. Kalimbetov
  • Marat A. Temirbekov
  • Zhanibek O. Khabibullayev

Abstract

The regularization method is applied for the construction of algorithm for an asymptotical solution for linear singular perturbed systems with the irreversible limit operator. The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first‐order partial differential equations with incomplete initial data.

Suggested Citation

  • Burkhan T. Kalimbetov & Marat A. Temirbekov & Zhanibek O. Khabibullayev, 2012. "Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:120192
    DOI: 10.1155/2012/120192
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    References listed on IDEAS

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    1. Ioan Gavrea & Mircea Ivan, 2011. "Asymptotic Behaviour of the Iterates of Positive Linear Operators," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-11, June.
    2. Fanglei Wang & Yukun An, 2011. "Positive Solutions for Singular Complementary Lidstone Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-13, December.
    3. Adelaida B. Vasil'eva & Leonid V. Kalachev, 2006. "Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-21, February.
    4. Adelaida B. Vasil′eva & Leonid V. Kalachev, 2006. "Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2006(1).
    5. Ioan Gavrea & Mircea Ivan, 2011. "Asymptotic Behaviour of the Iterates of Positive Linear Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    6. Fanglei Wang & Yukun An, 2011. "Positive Solutions for Singular Complementary Lidstone Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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    Cited by:

    1. M. De la Sen, 2013. "Some Results on Fixed and Best Proximity Points of Precyclic Self‐Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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