A note on continuous dependence of solutions of Volterra integral equations
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- Proc. Amer. Math. Soc. 81 (1981), 546-548 Request permission
Abstract:
The topologies induced by two families of seminorms on a vector space of functions $g:{R^ + } \times {R^ + } \times {E^n} \to {E^n}$ are compared. It is found that the continuous dependence of solutions of the Volterra equation $x(t) = f(t) + \int {_0^tg(t,s,x(s))ds}$ does not hold for the weaker topology. This result corrects an error in the book of Miller, Benjamin, Menlo Park, Calif., 1971.References
- Zvi Artstein, Continuous dependence of solutions of Volterra integral equations, SIAM J. Math. Anal. 6 (1975), 446–456. MR 361656, DOI 10.1137/0506039
- Richard K. Miller, Nonlinear Volterra integral equations, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Menlo Park, Calif., 1971. MR 0511193
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 546-548
- MSC: Primary 45D05; Secondary 45G10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0601726-5
- MathSciNet review: 601726