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Abstract volterra integrodifferential equations and a class of reaction-diffusion equations

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Volterra Equations

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. _____, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, 1976.

    Book  MATH  Google Scholar 

  3. M. G. Crandall, S.-O. Londen, and J. A. Nohel, An abstract nonlinear Volterra integrodifferential equation, J. Math. Anal. Appl. (to appear).

    Google Scholar 

  4. M. G. Crandall and J. A. Nohel, 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. A. Friedman, Partial differential equations, Holt, Rinehart, and Winston, New york, 1969.

    MATH  Google Scholar 

  6. _____, Monotonicity of solutions of Volterra integral equations in Banach space, Trans. Amer. Math. Soc. 138 (1969), 129–148.

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Friedman and M. Shinbrot, Volterra integral equations in Banach space, Trans. Amer. Math. Soc. 126 (1967), 131–179.

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Kato, Perturbation theory for linear operators, Springer-Verlag, New York, 1966.

    Book  MATH  Google Scholar 

  9. M. Loève, Probability theory. Foundations. Random sequences, 2nd rev. ed., University Series in Higher Math., Van Nostrand, Princeton, N. J., 1960.

    MATH  Google Scholar 

  10. S.-O. Londen, An existence result on a Volterra equation in a Banach space, Trans. Amer. Math. Soc. (to appear).

    Google Scholar 

  11. _____, On an integral equation in a Hilbert space, SIAM J. Math. Anal. (to appear).

    Google Scholar 

  12. S.-O. Londen and O. J. Staffans, A note on Volterra equations in a Hilbert space, Helsinki Univ. of Tech. Report-HTKK-MAT-A90 (1976).

    Google Scholar 

  13. R. C. MacCamy, Stability theorems for a class of functional differential equations, SIAM J. Math. Anal. (to appear).

    Google Scholar 

  14. _____, An integro-differential equation with applications in heat flow, Quart. Appl. Math. 35 (1977), 1–19.

    MathSciNet  MATH  Google Scholar 

  15. R. C. MacCamy and J. S. W. Wong, Stability theorems for some functional differential equations, Trans. Amer. Math. Soc. 164 (1972), 1–37.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. K. Miller, Volterra integral equations in a Banach space, Funkcial. Ekvac. 18 (1975), 163–194.

    MathSciNet  MATH  Google Scholar 

  17. R. K. Miller and R. L. Wheeler, Well-posedness and stability of linear Volterra integrodifferential equations in abstract spaces (to appear).

    Google Scholar 

  18. A. Pazy, Semi-groups of linear operators and applications to partial differential equations, Lecture Notes 10, University of Maryland (1974).

    Google Scholar 

  19. C. C. Travis and G. F. Webb, An abstract second order semilinear Volterra integrodifferential equation, SIAM J. Math. Anal. (to appear).

    Google Scholar 

  20. G. F. Webb, An abstract semilinear Volterra integrodifferential equation, Proc. Amer. Math. Soc. (to appear).

    Google Scholar 

  21. _____, Exponential representation of solutions to an abstract semi-linear differential equation, Pac. J. Math. 70 (1977), 269–280.

    Article  MathSciNet  MATH  Google Scholar 

  22. K. Yoshida, Functional analysis, Springer-Verlag, New York, 1968.

    Book  Google Scholar 

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Stig-Olof Londen Olof J. Staffans

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© 1979 Springer-Verlag

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Webb, G.F. (1979). Abstract volterra integrodifferential equations and a class of reaction-diffusion equations. In: Londen, SO., Staffans, O.J. (eds) Volterra Equations. Lecture Notes in Mathematics, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064516

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  • DOI: https://doi.org/10.1007/BFb0064516

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  • Print ISBN: 978-3-540-09534-7

  • Online ISBN: 978-3-540-35035-4

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