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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on Volterra equations in a Hilbert space


Authors: Stig-Olof Londen and Olof J. Staffans
Journal: Proc. Amer. Math. Soc. 70 (1978), 57-62
MSC: Primary 45N05; Secondary 47H15
MathSciNet review: 0467219
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Abstract | References | Similar Articles | Additional Information

Abstract: An existence and uniqueness result is given on the nonlinear Volterra equation

$\displaystyle u(t) + (a ^\ast Au)(t) \mathrel\backepsilon f(t),\quad t \in {R^ + },$

when considered in a real Hilbert space. The result extends earlier work by Barbu and Londen.

References [Enhancements On Off] (What's this?)

  • [1] 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 (52 #11666)
  • [2] Viorel Barbu, Nonlinear Volterra equations in a Hilbert space, SIAM J. Math. Anal. 6 (1975), 728–741. MR 0377620 (51 #13791)
  • [3] G. Gripenberg, An existence result for a nonlinear Volterra integral equation in Hilbert space, Report HTKK-MAT-A86, Helsinki University of Technology, 1976.
  • [4] Stig-Olof Londen, On an integral equation in a Hilbert space, SIAM J. Math. Anal. 8 (1977), no. 6, 950–970. MR 0511229 (58 #23401)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0467219-3
PII: S 0002-9939(1978)0467219-3
Keywords: Volterra equations, integral equations in Hilbert space
Article copyright: © Copyright 1978 American Mathematical Society