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Functional differential equations

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Analytic Theory of Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 183))

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References

  1. J.F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, N.J., 1964.

    MATH  Google Scholar 

  2. W.A. Harris and Y. Sibuya, On asymptotic solutions of systems of difference equations, J. Reine Angew. Math. 222 (1966), 120–135.

    MathSciNet  MATH  Google Scholar 

  3. J. Hurt, Some aspects of difference equations, Ph.D. Thesis, Brown University, June 1967.

    Google Scholar 

  4. R. Bellman and K. Cooke, Differential-Difference Equations, Academic Press, 1963.

    Google Scholar 

  5. Trudy Seminara po Teorii Differentialnix Uravneniya c Otklonyayuskekimsya Argumentom, Vols. 1–7 (1962–1969), Univ. Druz. Narodov Patrisa Lymumbi, Moscow.

    Google Scholar 

  6. A.M. Zverkin, G.A. Kamenskii, S.B. Norkin and L.E. El'sgolt'z, Differential equations with retarded arguments, Uspehi Mat. Nauk 17 (1962), 77–164.

    MathSciNet  Google Scholar 

  7. R. Driver, Existence and continuous dependence of solutions of a neutral functional differential equation, Arch. Rational Mech. Anal. 19 (1965), 149–166.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  9. J.K. Hale and M.A. Cruz, Existence, uniqueness, and continuous dependence for hereditary systems, Ann. Mat. Pura Appl. (to appear).

    Google Scholar 

  10. G. Prada and T.A. Bickert, Stability of electrical networks containing distributed RC networks (to appear).

    Google Scholar 

  11. K.L. Cooke and D.W. Krumme, Differential-difference equations and nonlinear initial-value problems for linear hyperbolic partial differential equations, J. Math. Anal. Appl. 24 (1968), 372–387.

    Article  MathSciNet  MATH  Google Scholar 

  12. J.K. Hale, Forward and backward existence for neutral functional differential equations, J. Differential Equations (to appear).

    Google Scholar 

  13. N.N. Krasovskii, Stability of Motion, Stanford Univ. Press, 1963.

    Google Scholar 

  14. A. Halanay, Differential Equations, Academic Press, 1966.

    Google Scholar 

  15. J.K. Hale, Sufficient conditions for stability and instability of autonomous functional differential equations, J. Differential Equations 1 (1965), 452–482.

    Article  MathSciNet  MATH  Google Scholar 

  16. B.D. Coleman and V.J. Mizel, On the stability of solutions of functional differential equations, Arch. Rational Mech. Anal. 30 (1968), 173–196.

    MathSciNet  MATH  Google Scholar 

  17. J.K. Hale and C. Perello, The neighborhood of a singular point of functional differential equations, Contributions to Differential Equations 3 (1964), 351–375.

    MathSciNet  MATH  Google Scholar 

  18. A. Stokes, On the stability of a limit cycle of an autonomous functional differential equation, Contributions to Differential Equations 3 (1964), 121–140.

    MathSciNet  MATH  Google Scholar 

  19. J.K. Hale, Geometric theory of functional differential equations, Differential Equations and Dynamical Systems, Academic Press, 1967.

    Google Scholar 

  20. W. Oliva, Functional differential equations on a compact manifold and an approximation theorem, J. Differential Equations 5 (1969), 483–496.

    Article  MathSciNet  MATH  Google Scholar 

  21. R.B. Grafton, A periodicity theorem for autonomous functional differential equations, J. Differential Equations 6 (1969), 87–109.

    Article  MathSciNet  MATH  Google Scholar 

  22. S. Bancroft, Boundary value problems for functional differential equations, Ph.D. Thesis, Brown University, June 1968.

    Google Scholar 

  23. D. Henry, The adjoint linear functional equation, J. Differential Equations (to appear).

    Google Scholar 

  24. N. Chafee, A bifurcation problem for a functional differential equation of finitely retarded type (to appear).

    Google Scholar 

  25. J.K. Hale, Solutions near simple periodic orbits of functional differential equations, J. Differential Equations 7 (1970), 126–138.

    Article  MathSciNet  MATH  Google Scholar 

  26. M.A. Cruz and J.K. Hale, Stability of functional differential equations, J. Differential Equations 7 (1970), 334–355.

    Article  MathSciNet  MATH  Google Scholar 

  27. M.A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, MacMillan, 1964.

    Google Scholar 

  28. M. Slemrod, Nonexistence of oscillations in a nonlinear distributed network, J. Math. Anal. Appl. (to appear).

    Google Scholar 

  29. M.A. Cruz and J.K. Hale, Exponential estimates and the saddle point property for neutral functional differential equations, J. Math. Anal. Appl. (to appear).

    Google Scholar 

  30. J.K. Hale, Critical cases for neutral functional differential equations, J. Differential Equations, (to appear).

    Google Scholar 

  31. D. Henry, Small solutions of linear autonomous functional differential equations, J. Differential Equations (to appear).

    Google Scholar 

  32. J.A. Yorke and E. Winston, Linear delay differential equations whose solutions become identically zero, Rev. Roumaine Math. Pures Appl. 14 (1969), 885–887.

    MathSciNet  MATH  Google Scholar 

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P. F. Hsieh A. W. J. Stoddart

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© 1971 Springer-Verlag

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Hale, J.K. (1971). Functional differential equations. In: Hsieh, P.F., Stoddart, A.W.J. (eds) Analytic Theory of Differential Equations. Lecture Notes in Mathematics, vol 183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060406

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  • DOI: https://doi.org/10.1007/BFb0060406

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05369-9

  • Online ISBN: 978-3-540-36454-2

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