Hiroshima Mathematical Journal

Volterra integral equations as functional differential equations on infinite intervals

G. F. Webb

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 7, Number 1 (1977), 61-70.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206135949

Digital Object Identifier
doi:10.32917/hmj/1206135949

Mathematical Reviews number (MathSciNet)
MR0445247

Zentralblatt MATH identifier
0352.45002

Subjects
Primary: 45D05: Volterra integral equations [See also 34A12]
Secondary: 34K05: General theory 34G05

Citation

Webb, G. F. Volterra integral equations as functional differential equations on infinite intervals. Hiroshima Math. J. 7 (1977), no. 1, 61--70. doi:10.32917/hmj/1206135949. https://projecteuclid.org/euclid.hmj/1206135949


Export citation

References

  • [1] V. Barbu and S. I. Grossman, "Asymptotic behavior of linear integrodifferential systems," Trans. Amer. Math. Soc., 173 (1972), 277-287.
  • [2] D. W. Brewer, "A nonlinear semigroup for a functional differential equation," thesis, University of Wisconsin-Madison, 1975.
  • [3] J. A. Burns and T. L. Herdman, "Adjoint semigroup theory for a Volterra integrodifferential system," Bull. Amer. Math. Soc., 81 (1975), 1099-1102.
  • [4] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience, New York, 1957.
  • [5] J. Dyson and R. Villella Bressan, "Functional differential equations and nonlinear evolution operators," Edinburgh Jour. Math. 75 A, 20 (1975/76), 223-234.
  • [6] W. Fitzgibbon, "Time dependent perturbations of linear accretive operators," to appear.
  • [7] W. Fitzgibbon, "Stability for abstract nonlinear Volterra equations involving finite delay," to appear.
  • [8] R. Grimmer and G. Seifert, "Stability properties of Volterra integrodifferential equations," Jour. Diff. Eqs., 19 (1975), 142-166.
  • [9] J. Hale, "Functional differential equations with infinite delays," Jour. Math. Anal. Appl. 48 (1974), 276-283.
  • [10] A. Ize and A. Freiria, "Asymptotic behavior and nonoscillation of Volterra integral equations and functional differential equations," Proc. Amer. Math. Soc., 52 (1975), 169-177.
  • [11] R. Martin, "Nonlinear perturbations of linear evolution systems," to appear.
  • [12] K. Maruo and N. Yamada, "A remark on integral equations in a Banach space," Proc. Japan Academy, 49 (1973), 13-16.
  • [13] R. K. Miller, "Linear Volterra integrodifferential equations as semigroups," Funkcial. Ekvac., 17 (1974), 39-55.
  • [14] N. Pavel, "On an integral equation," Rev. Roum. Math. Pures et Appl., 19 (1974), 237-244.
  • [15] A. T. Plant, "Nonlinear semigroups of translantions in Banach spaces generated by functional differential equations," to appear.
  • [16] G.F.Webb, "Continuous nonlinear perturbations of linear accretive operators in Banach spaces," Jour. Functional Analysis, 10 (1972), 191-203.
  • [17] G. F. Webb, "Functional differential equations and nonlinear semigroups in Lp - spaces," Jour. Diff. Eqs., 20 (1976), 71-89.
  • [18] G.F.Webb, "Linear functional differential equations with L2 initial functions," Funkcial. Ekvac., to appear.
  • [19] G. F. Webb, "Numerical approximation of nonlinearfunctional differential equations with L2 initial functions," to appear.