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Nonlinear neutral functional differential equations in product spaces

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References

  1. J. M. Amillo Gil, J. A. Burns and E. M. Cliff, Approximation of nonlinear neutral functional differential equations on product spaces, preprint.

    Google Scholar 

  2. J. Amillo Gil, Nonlinear Neutral Functional Differential Equations on Product Spaces, Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, August 1981.

    Google Scholar 

  3. H. T. Banks, Approximation of nonlinear functional differential equation control systems, J. Optimization Theory Appl., 29 (1979), 383–408.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. H. T. Banks, Identification of nonlinear delay systems using spline methods, International Conference on Nonlinear Phenomena in the Mathematical Sciences, University of Texas, Arlington, Texas, June 16–20, 1980.

    Google Scholar 

  5. H. T. Banks and J. A. Burns, Hereditary control problems: Numerical methods based on averaging approximations, SIAM J. Control and Optimization, 16, (1978), 169–208.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. H. T. Banks, J. A. Burns and E. M. Cliff, Spline-based approximation methods for control and identification of hereditary systems, in Intl. Symp. on Systems Optimization and Analysis, A. Beusousan and J. L. Lions, Eds., Lecture Notes in Control and Info. Sci. Vol. 14, Springer, Heildeberg, 1979, 314–320.

    CrossRef  Google Scholar 

  7. H. T. Banks, J. A. Burns and E. M. Cliff, Parameter estimation and identification for systems with delays, SIAM J. Control and Optimization, 19 (1981), 791–828.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. H. T. Banks and F. Kappel, Spline approximations for functional differential equations, J. Diff. Eqs., 34 (1979), 496–522.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. J. A. Burns and E. M. Cliff, Hereditary models for airfoils in unsteady aerodynamics, numerical approximations and parameter estimation, AFWAL Technical Report, Wright-Patterson AFB, Ohio, 1981, to appear.

    Google Scholar 

  10. J. A. Burns and E. M. Cliff, An approximation technique for the control and identification of hybrid systems, Proc. Third AIAA Symposium on Dynamics and Control of Large Flexible Spacecraft, L. Meirovitch, Ed., June 1981, 269–284.

    Google Scholar 

  11. J. A. Burns, T. L. Herdman and H. W. Stech. Linear functional differential equations as semigroups on product spaces, SIAM J. Math. Anal., in press.

    Google Scholar 

  12. J. A. Burns, T. L. Herdman and H. W. Stech, Differential-boundary operators and associated neutral functional differential equations, Rocky Mountain J. Math., in press.

    Google Scholar 

  13. J. A. Burns, T. L. Herdman and H. W. Stech, The Cauchy problem for linear functional differential equations, in Integral and Functional Differential Equations, T. L. Herdman, S. M. Rankin and H. W. Stech, Eds., Marcel Dekker, 1981, 137–147.

    Google Scholar 

  14. R. K. Brayton and W. L. Miranker, A stability theory for nonlinear mixed initial boundary value problems. Arch. Rational Mech. Anal. 17 (1964), 358–376.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. R. K. Brayton and R. A. Willoughby, On the numerical integration of difference-differential equations of neutral type, J. Math. Anal. Appl., 18 (1967), 182–189.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. J. Hale, Theory of Functional DIfferential Equations, Springer-Verlag, New York, 1977.

    CrossRef  MATH  Google Scholar 

  18. F. Kappel, Approximation of neutral functional differential equations in the state space R n × L 2, Colloquia Mathematica Societatis János Bolyai, 30. Qualitative Theory of Differential Equations, Szeged (Hungary), 1979, 463–506.

    Google Scholar 

  19. F. Kappel, An approximation scheme for delay equations, Proc. Int'l Conference on Nonlinear Phenomena in Mathematical Sciences, Arlington, Texas, June 1980, in press.

    Google Scholar 

  20. F. Kappel and K. Kunisch, Spline approximations for neutral functional differential equations, SIAM J. Numer. Anal., 18 (1981), 1058–1080.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. K. Kunisch, Neutral functional differential equations in L p-spaces and averaging approximations, J. Nonlinear Anal. TMA 3 (1979), 419–448.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. K. Kunish, Approximation schemes for nonlinear neutral optimal control systems, J. Math., Anal. Appl., 82 (1981), 112–143.

    CrossRef  MathSciNet  Google Scholar 

  23. O. Lopes, Forced occillations in nonlinear neutral differential equations, SIAM J. Appl. Math., 29 (1975), 196–207.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. R. M. Reid, Ph.D. Thesis, Department of Mathematics, University of Wisconsin, Madison, Wisconsin, August, 1979.

    Google Scholar 

  25. D. L. Russell, "Control canonical structure for a class of distributed parameter systems," Proc. Third IMA Conference on Control Theory, Sheffield, September 1980.

    Google Scholar 

  26. D. L. Russell, "Closed-loop eigenvalue specification for infinite dimensional systems: augmented and deficient hyperbolic cases," Technical Summary Report #2021, Mathematics Research Center, University of Wisconsin, Madison, August 1979.

    Google Scholar 

  27. M. H. Schultz, Spline analysis, Prentice Hall, Englewood Cliffs, NJ, 1973.

    MATH  Google Scholar 

  28. R. G. Teglas, A control canonical form for a class of linear hyperbolic systems, Ph.D. Thesis, Mathematics Department, University of Wisconsin, Madison, Wiscons, June 1981.

    Google Scholar 

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Amillo Gil, J.M., Burns, J.A., Cliff, E.M. (1982). Nonlinear neutral functional differential equations in product spaces. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064993

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  • DOI: https://doi.org/10.1007/BFb0064993

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