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Nonlinear vector-valued hereditary equations on the line

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Volterra Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 737))

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References

  1. Barbu, V. "Nonlinear Volterra equations in Hilbert space", Siam J. Math. Anal. 6 (1975), 728–741.

    Article  MathSciNet  MATH  Google Scholar 

  2. Barbu, V., Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing, Leyden, 1976.

    Book  MATH  Google Scholar 

  3. Corduneanu, C., Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.

    MATH  Google Scholar 

  4. Crandall, M. G. and Nohel, J. A., "An abstract functional differential equation and a related nonlinear Volterra equation", Math. Res. Center, Univ. of Wisconsin, Tech. Summary Report #1765 (1977).

    Google Scholar 

  5. Gripenberg, G., "An existence result for a nonlinear Volterra integral equation in Hilbert space", Siam J. Math. Anal. (to appear).

    Google Scholar 

  6. Komura, Y., "Nonlinear semigroups in Hilbert spaces", J. Math. Soc. Japan 19 (1967), 493–507.

    Article  MathSciNet  MATH  Google Scholar 

  7. Leitman, M. J. and Mizel, V. J., "On fading memory spaces and hereditary integral equations", Arch. Rat. Mech. Anal. 55 (1974), 18–51.

    Article  MathSciNet  MATH  Google Scholar 

  8. Leitman, M. J. and Mizel, V. J., "Hereditary laws and nonlinear integral equations on the line", Adv. in Math. 22 (1976), 220–266.

    Article  MathSciNet  MATH  Google Scholar 

  9. Leitman, M. J. and Mizel, V. J., "Asymptotic stability and the periodic solutions of x(t) + ∫ t-∞ a(t-s)g(s,x(s))ds = f(t), J. Math. Anal. Appl. (to appear), also in Technion Preprint Series #MT-339 (1977).

    Google Scholar 

  10. Levin, J. J., "On a nonlinear Volterra equation", J. Math. Anal. Appl. 39 (1972), 458–476.

    Article  MathSciNet  MATH  Google Scholar 

  11. Levin, J. J., "Some a'priori bounds for nonlinear Volterra equations", Siam J. Math. Anal. 7 (1976), 872–897.

    Article  MathSciNet  MATH  Google Scholar 

  12. Levin, J. J. and Shea, D. F., "On the asymptotic behavior of some integral equations I, II, III", J. Math. Anal. Appl. 37 (1972), 42–82, 288–326, 537–575.

    Article  MathSciNet  MATH  Google Scholar 

  13. Londen, S.-O., "On an integral equation in a Hilbert space", Siam J. Math. Anal. (to appear).

    Google Scholar 

  14. MacCamy, R.C., "Nonlinear Volterra equations on a Hilbert space", J. Diff. Eqns. 16 (1974), 373–393.

    Article  MathSciNet  MATH  Google Scholar 

  15. MacCamy, R. C., "Remarks on frequency domain methods for Volterra integral equations", J. Math. Anal. Appl. 55 (1976), 555–575.

    Article  MathSciNet  MATH  Google Scholar 

  16. MacCamy, R. C., "An integro-differential equation with application in heat flow", Q. Appl. Math. 35 (1977), 1–19.

    MathSciNet  MATH  Google Scholar 

  17. MacCamy, R. C. and Weiss, P., "Qualitative numerical theory for Volterra equations", these proceedings.

    Google Scholar 

  18. MacCamy, R. C. and Smith, R. L., "Limits of solutions of nonlinear Volterra equations", Applic. Anal. (1977), 19–27.

    Google Scholar 

  19. Miller, R. K. and Sell, G. R., "The topological dynamics of Volterra integral equations", Proc. of Conf. for Qual. Th. Nonlin. Diff. and Inteq. Eqns., Madison, Wisconsin, (1968).

    Google Scholar 

  20. Miller, R. K. and Sell, G. R., Volterra Integral Equations and Topological Dynamics, Mem. Am. Math. Soc. 102 (1970).

    Google Scholar 

  21. Miller, R. K., Nonlinear Volterra Integral Equations, Benjamin, Menlo Park, 1971.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

    R. C. MacCamy & Victor J. Mizel

Authors
  1. R. C. MacCamy
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  2. Victor J. Mizel
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Stig-Olof Londen Olof J. Staffans

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© 1979 Springer-Verlag

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MacCamy, R.C., Mizel, V.J. (1979). Nonlinear vector-valued hereditary equations on the line. In: Londen, SO., Staffans, O.J. (eds) Volterra Equations. Lecture Notes in Mathematics, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064508

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  • DOI: https://doi.org/10.1007/BFb0064508

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09534-7

  • Online ISBN: 978-3-540-35035-4

  • eBook Packages: Springer Book Archive

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