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Solutions of systems of nonlinear functional-differential equations bounded in the entire real axis and their properties

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Abstract

For a system of nonlinear functional-differential equations with a linearly transformed argument, we establish the existence and uniqueness conditions for a solution bounded in the entire real axis and study the properties of this solution.

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References

  1. L. J. Grimm, “Existence and continuous dependence for a class of nonlinear neutral-differential equations,”Proc. Am. Math. Soc.,29, No. 3, 467–473 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Kwapisz, “On the existence and uniqueness of solutions of a certain integral-functional equation,”Ann. Pol. Math.,31, No. 1, 23–41 (1975).

    MATH  MathSciNet  Google Scholar 

  3. T. Kato and J. B. McLeod, “The functional-differential equationy′(x)=ay(λx)+by(x),”Bull. Am. Math. Soc.,77, 891–937 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  4. Yu. A. Mitropol'skii, A. M. Samoilenko, and D. I. Martynyuk,Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients [in Russian], Naukova Dumka, Kiev (1985);English translation Kluwer AP, Dordrecht (1993).

    Google Scholar 

  5. V. S. Mokeichev,Differential Equations with Deviating Arguments [in Russian], Kazan University, Kazan (1985).

    Google Scholar 

  6. R. Bellman and K. L. Cooke,Differential-Difference Equations, Academic Press, New York (1963).

    MATH  Google Scholar 

  7. V. B. Kolmanovskii and V. R. Nosov,Stability and Periodic Modes of Controlled Systems with Aftereffect [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  8. J. Hale,Theory of Functional Differential Equations, Springer Verlag, Berlin (1977).

    MATH  Google Scholar 

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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 737–747, June, 1994.

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Samoilenko, A.M., Pelyukh, G.P. Solutions of systems of nonlinear functional-differential equations bounded in the entire real axis and their properties. Ukr Math J 46, 799–811 (1994). https://doi.org/10.1007/BF02658181

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  • DOI: https://doi.org/10.1007/BF02658181

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