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Integral equations with a delay

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References

  1. Leigh C. Becker, T. A. Burton and S. Zhang, Functional differential equations and Jensen's inequality, J. Math. Anal. Appl., 138 (1989), 137–156.

    Google Scholar 

  2. S. N. Busenberg and K. L. Cooke, Stability conditions for linear non-autonomous delay differential equations, Quart. Appl. Math., 42 (1984), 295–306.

    Google Scholar 

  3. T. A. Burton, A. Casal and A. Somolinos, Upper and lower bounds for Liapunov functionals, Funkcialaj Ekvacioj, 32 (1989), 23–55.

    Google Scholar 

  4. T. A. Burton and R. H. Hering, Liapunov theory for functional differential equations, Rocky Mountain J. Math., 24 (1994), 3–17.

    Google Scholar 

  5. T. A. Burton and Laszlo Hatvani, Stability theorems for nonautonomous functional differential equations by Liapunov functionals, Tohoku Math. J., 41 (1989), 65–104.

    Google Scholar 

  6. T. A. Burton and G. Makay, Asymptotic stability for functional differential equations, Acta Math. Hungar., 65 (1994), 243–251.

    Google Scholar 

  7. J. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations, Springer (New York, 1993).

    Google Scholar 

  8. L. Hatvani, Asymptotic stability conditions for a linear nonautonomous delay differential equation, preprint.

  9. L. Hatvani and T. Krisztin, Asymptotic stability for a differential-difference equation containing both delayed and undelayed terms, Acta Sci. Math. (Szeged), 60 (1995), 371–384.

    Google Scholar 

  10. D. R. Smart, Fixed Point Theorems, Cambridge Univ. Press (Cambridge, 1980).

    Google Scholar 

  11. Tingxiu Wang, Equivalent conditions on stability of functional differential equations, J. Math. Anal. Appl., 170 (1992), 138–157.

    Google Scholar 

  12. Tingxiu Wang, Upper bounds for Liapunov functionals, integral Lipschitz condition and asymptotic stability, Differential and Integral Equations, 7, (1994), 441–452.

    Google Scholar 

  13. Tingxiu Wang, Asymptotic stability and the derivatives of solutions of functional differential equations, Rocky Mountain J. Math., 24 (1994), 403–427.

    Google Scholar 

  14. Tingxiu Wang, Weakening the condition W 1(|ø(0)|)≦V(t, ø)≦W 2(‖ø‖) for uniform asymptotic stability, Nonlinear Analysis, 23 (1994), 251–264.

    Google Scholar 

  15. YoshizawaT., Asymptotic behaviors of solutions of differential equations, in Differential equations:qualitative theory, Colloq. Math. Soc. János Bolyai 47, North-Holland (Amsterdam, 1987), pp. 1141–1164.

    Google Scholar 

  16. Bo Zhang, Asymptotic stability in functional differential equations by Liapunov functionals, Trans. Amer. Math. Soc., 347 (1995), 1375–1382.

    Google Scholar 

  17. Bo Zhang, A stability theorem in functional differential equations, Differential and Integral Equations, to appear.

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  1. Department of Mathematics, Southern Illinois University, 62901, Carbondale, IL, U.S.A.

    T. A. Burton

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  1. T. A. Burton
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Burton, T.A. Integral equations with a delay. Acta Math Hung 72, 233–242 (1996). https://doi.org/10.1007/BF00050686

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  • DOI: https://doi.org/10.1007/BF00050686

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