Journal of Applied Mathematics and Computing

, Volume 10, Issue 1–2, pp 75–81 | Cite as

Lipschitz stability criteria for a generalized delayed Kolmogorov model



Lipschitz stability and Lipschitzϕ - equistability of the functional differential equation\(x' = B(x)f(t,x,x_t ), x_{t_ \circ = \theta _ \circ } \) are discussed. Sufficient conditions are given using the comparison with the corresponding scalar equation.

AMS Mathematics Subject Classification

34D20 34C11 

Key words and phrases

Lipschitz stability ϕ - equistability comparison method 


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  1. 1.
    E.P. Akpan, and O. Akingele,On the ϕ -stability of comparison differential system, J. Math. Anal. Appl. 164 (1992), 307–324.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    E.P. Akpan,On the ϕ -stability of functional differential equations, I international center for theoretical Physics, Miramare-Trieste 180 (1993).Google Scholar
  3. 3.
    F. Dannan and Elaydi,Lipschitz stability of nonlinear systems of differential equations, J. Math. Anal. Appl. 113 (1986), 562–577.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    M.M.A. El-Sheikh, and A.A. Soliman,On Lipschitz stability for nonlinear systems of ordinary differential equations, J. Differential Equations and Dynamical Systems Vol. 3 No. 3, (1995). 235–250.MATHMathSciNetGoogle Scholar
  5. 5.
    M.M.A. El-Sheikh, and A.A. Soliman,ϕ - stabilitycriteria of nonlinear systems of differential equations, J. Pan Amer. Math. reprint.Google Scholar
  6. 6.
    H.I. Freedman,A perturbed Kolmogrov-type model for the growth problem, Math. Biosci. 12, (1975), 721–732.Google Scholar
  7. 7.
    H.I. Freedman, and A.A. Martynyuk,Boundedness criteria for solutions of perturbed Kolmogrov population models, J. Canadian Applied Math. Quart. Vol. 3, No. 2 (1995) 203–217.MATHMathSciNetGoogle Scholar
  8. 8.
    V. Lakshmikantham and S. Leela,Differential and integral inequalities, Vol. II, Academic press, New York, and London 1969.MATHGoogle Scholar
  9. 9.
    V. Lakshmikantham and Xinzhi Liu,On asymptotic stability for nonautonomous differential systems, J. Nonlinear Anal. Theory, Methods, Appl. Vol. 13, No. 10 (1989), 1181–1189.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    M.A. Sattar and G. Bojadziev,Perturbation in the three dimensional Kolmogorov model, Math. Biosci 78 (1986), 293–305.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    M.A. Sttar and G. Bojadziev,Bifurcations in the three dimensional Kolmogorov model, Math. Biosci 86 (1987), 51–66.CrossRefMathSciNetGoogle Scholar
  12. 12.
    Yu-Li Fu,On Lipschitz stability for F.D.E, Pacific Journal of Mathematics, Vol. 151, No. 2, (1991), 229–235.MATHMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2002

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceMenoufia UniversityShebin El-KoomEgypt

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