Computational Mathematics and Modeling

, Volume 25, Issue 4, pp 484–499 | Cite as

Asymptotic Behavior of Regularized Solutions of One Model of Economic Growth with Delay

  • P. G. Surkov

We consider an ill-posed problem to find the solutions of an economic growth model with a delay. Asymptotic formulas are constructed for regularized solutions of the delayed system on a finite interval on the negative half-axis.


optimal control economic dynamics models 


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  1. 1.
    J. Murray, Nonlinear Differential Equations in Biology [Russian translation], Mir, Moscow (1983).Google Scholar
  2. 2.
    K. C. Velupillai and N. Dharmaraj, The Time-to-Build Tradition in Business Cycle Modelling, ASSRU Discussion Paper 09–11, Trento (March 2011).Google Scholar
  3. 3.
    S. Ruan, “On nonlinear dynamics of predator-prey models with discrete delay,” Math. Model. Nat. Phenom., 4, No. 2, 140–188 (2009).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    J. Maynard-Smith, Models in Ecology [Russian translation], Mir, Moscow (1976).Google Scholar
  5. 5.
    R. M. Goodwin, “A growth cycle,” in: Socialism, Capitalism and Economic Growth, Cambridge Univ. Press (1967).Google Scholar
  6. 6.
    V. Volterra, Mathematical Theory of the Struggle for Survival [Russian translation], Nauka, Moscow (1976).Google Scholar
  7. 7.
    Report on the State and Preservation of the Environment in Vologda Province in 2006 [in Russian], Vologda Provincial Government, Department of Natural Resources and Preservation of the Environment of the Vologda Province, Vologda (2007).Google Scholar
  8. 8.
    A. Yu. Kolesov and Yu. S. Kolesov, “Relaxation oscillations in mathematical models in ecology,” Trudy Mat. Inst. im. V. A. Steklov, Vol. 199 (1993).Google Scholar
  9. 9.
    A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems [in Russian], Nauka, Moscow 1986.Google Scholar
  10. 10.
    Yu. F. Dolgii and P. G. Surkov, “Ill-posed problem of reconstruction of the population size in Hutchinsons mathematical model,” Trudy Inst. Matem. Mekhan. UrORAN, 17, No. 1, 70–84 (2011).Google Scholar
  11. 11.
    M. M. Vainberg, Variational Method and the Method of Monotone Operators [in Russian], Nauka, Moscow (1972).Google Scholar
  12. 12.
    Rapoport, On Some Asymptotic Methods for Ordinary Differential Equations [in Russian], Nauka, Moscow (1953).Google Scholar
  13. 13.
    J. Hale, Theory of Functional Differential Equations [Russian translation], Mir (1984).Google Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsUral Branch of the Russian Academy of ScienceEkaterinburgRussia

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