## Hiroshima Mathematical Journal

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

### Volterra integral equations as functional differential equations on infinite intervals

**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

#### 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.Zentralblatt MATH: 0333.34057
- [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.Zentralblatt MATH: 0084.10402
- [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.Mathematical Reviews (MathSciNet): MR463826
- [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.Zentralblatt MATH: 0285.34046
- [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.Zentralblatt MATH: 0405.65052

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