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Abstract Cauchy problem and abstract integral equations for neutral functional differential equations

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References

  1. H. T.Banks, Approximation methods for optimal control problems with delay differential systems. Seminaires IRIA: analyse et controle de systemes 5–19 (1976).

  2. H. T. Banks andJ. A. Burns, Hereditary control problems: numerical methods based on averaging approximations. SIAM J. Control and Optimization16, 169–208 (1978).

    Google Scholar 

  3. V.Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces. 1976.

  4. R. Brayton, Small signal stability criterion for electrical networks containing lossless transmission lines. IBM J. Res. Dev.12, 431–440 (1968).

    Google Scholar 

  5. N.Dunford and J. T.Schwarz, Linear Operators I, 1966.

  6. A. Halanay andVl. Rasvan, Periodic and almost periodic solutions for a class of systems described by delay-differential and difference equations. Nonlinear Analysis TMA1, 197–206 (1977).

    Google Scholar 

  7. J.Hale, Theory of Functional Differential Equations. Berlin-Heidelberg-New York 1977.

  8. J. K. Hale andM. A. Cruz, Existence, uniqueness and continuous dependence for hereditary systems. Ann. Mat. pura appl. (IV)85, 63–82 (1970).

    Google Scholar 

  9. J. K.Hale and K. R.Meyer, A class of functional equations of neutral type. Mem. Amer. Math. Soc. No.76 (1967).

  10. E.Hewitt and K.Stromberg, Real and Abstract Analysis. Berlin-Heidelberg-New York 1965.

  11. F. Kappel andW. Schappaciier, Autonomous functional differential equations and averaging approximations. Nonlinear Analysis TMA2, 391–422 (1978).

    Google Scholar 

  12. F.Kappel and W.Schappacher, Nonlinear functional differential equations and abstract integral equations, submitted to Edinburgh J. Math.

  13. K.Kunisch, Neutrale Funktional-Differentialgleichungen und Halbgruppentheorie. Berichte der Math.-Stat. Sektion im Forschungszentrum Graz, No.81 (1977).

  14. K.Kunisch, Neutral functional differential equations inL P-spaces and averaging approximations, to appear: Nonlinear Analysis TMA.

  15. Vl. Rasvan, Absolute stability of a class of nonlinear time lag control systems 1. Rev. Roum. Sci. Techn.-Electrotechnique Energ.17, 667–681 (1972).

    Google Scholar 

  16. O. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach space. J. Functional Analysis10, 191–203 (1972).

    Google Scholar 

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  1. Karl Kunisch

    Present address: Institut für Mathematik 2, Technische Universität, A-8010, Graz, Austria

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    Kunisch, K. Abstract Cauchy problem and abstract integral equations for neutral functional differential equations. Arch. Math 31, 580–588 (1978). https://doi.org/10.1007/BF01226495

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