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Stability in functional differential equations

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Functional Differential Equations and Bifurcation

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 799))

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References

  1. BARNEA, B.I., A method and new results for stability and instability of autonomous functional differential equations, SIAM J. Appl. Math., 17(1969), 681–697.

    Article  MathSciNet  MATH  Google Scholar 

  2. BURTON, T.A., Uniform asymptotic stability in functional differential equations, Proc. Amer. Math. Soc., 68(1978), 195–199.

    Article  MathSciNet  MATH  Google Scholar 

  3. DIVER, R.D., Existence and stability of solutions of a delay-differential system, Arch. Rational Mech. Anal., 10(1962), 401–426.

    Article  ADS  MathSciNet  Google Scholar 

  4. GRIMMER, R. and SEIFERT, G., Stability properties of Volterra integro-differential equations, J. Differential Eqs., 19(1975), 142–166.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. HALE, J.K., Theory of Functional Differential Equations, Appl. Math. Sci., Vol. 3, Springer-Verlag, 1977.

    Google Scholar 

  6. HALE, J.K. and KATO, J., Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21(1978), 11–41.

    MathSciNet  MATH  Google Scholar 

  7. KATO, J., On Liapunov-Razumikhin type theorems for functional differential equations, Funkcial. Ekvac., 16(1973), 225–239.

    MathSciNet  MATH  Google Scholar 

  8. KATO, J., Stability problem in functional differential equations with infinite delay, Funkcial. Ekvac., 21(1978), 63–80.

    MathSciNet  MATH  Google Scholar 

  9. KATO, J., Liapunov's second method in functional differential equations, to appear.

    Google Scholar 

  10. KRASOVSKII, N.N., Stability of Motion, Stanford Univ. Press, 1963.

    Google Scholar 

  11. LAKSHMIKANTHAM, V. and LEELA, S., Differential and Integral Inequalities, Vol. 2, Academic Press, 1969.

    Google Scholar 

  12. LEVIN, J.J., The asymptotic behavior of the solution of a Volterra equation, Proc. Amer. Math. Soc., 14(1963), 534–541.

    Article  MathSciNet  MATH  Google Scholar 

  13. LEVIN, J.J. and NOHEL, J.A., Perturbations of a nonlinear Volterra equation, Michigan Math. J., 12(1965), 431–447.

    Article  MathSciNet  MATH  Google Scholar 

  14. MILLER, R.K., Asymptotic stability properties of linear Volterra integro-differential equations, J. Differential Eqs., 10(1971), 485–506.

    Article  ADS  MATH  Google Scholar 

  15. NAITO, T., On autonomous linear functional differential equations with infinite retardations, J. Differential Eqs., 21(1976), 297–315.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. RAZUMIKHIN, B.S., On the stability of systems with a delay, Prikl. Mat. Meh., 20(1956), 500–512.

    MathSciNet  Google Scholar 

  17. SEIFERT, G., Liapunov-Razumikhin conditions for asymptotic stability in functional differential equations of Volterra type, J. Differential Eqs., 16(1974), 289–297.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. WRIGHT, E.M., A nonlinear difference-differential equation, J. Reine Angew. Math., 194(1955), 66–87.

    MathSciNet  MATH  Google Scholar 

  19. YOSHIZAWA, T., Stability theory by Liapunov's second method, Japan Math. Soc. Publ., Vol. 9, 1966.

    Google Scholar 

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Antonio Fernandes Izé

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© 1980 Springer-Verlag

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Kato, J. (1980). Stability in functional differential equations. In: Izé, A.F. (eds) Functional Differential Equations and Bifurcation. Lecture Notes in Mathematics, vol 799. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089317

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  • DOI: https://doi.org/10.1007/BFb0089317

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09986-4

  • Online ISBN: 978-3-540-39251-4

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