A note on Volterra equations in a Hilbert space
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- by Stig-Olof Londen and Olof J. Staffans PDF
- Proc. Amer. Math. Soc. 70 (1978), 57-62 Request permission
Abstract:
An existence and uniqueness result is given on the nonlinear Volterra equation \[ u(t) + (a ^\ast Au)(t) \backepsilon f(t),\quad t \in {R^ + },\] when considered in a real Hilbert space. The result extends earlier work by Barbu and Londen.References
- Viorel Barbu, Nonlinear semigroups and differential equations in Banach spaces, Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff International Publishing, Leiden, 1976. Translated from the Romanian. MR 0390843
- Viorel Barbu, Nonlinear Volterra equations in a Hilbert space, SIAM J. Math. Anal. 6 (1975), 728–741. MR 377620, DOI 10.1137/0506064 G. Gripenberg, An existence result for a nonlinear Volterra integral equation in Hilbert space, Report HTKK-MAT-A86, Helsinki University of Technology, 1976.
- Stig-Olof Londen, On an integral equation in a Hilbert space, SIAM J. Math. Anal. 8 (1977), no. 6, 950–970. MR 511229, DOI 10.1137/0508073
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 70 (1978), 57-62
- MSC: Primary 45N05; Secondary 47H15
- DOI: https://doi.org/10.1090/S0002-9939-1978-0467219-3
- MathSciNet review: 0467219