Periodic -solutions of an integrodifferential equation in a Hilbert space

Author:
Olof J. Staffans

Journal:
Proc. Amer. Math. Soc. **117** (1993), 745-751

MSC:
Primary 45J05; Secondary 34K15, 47G10, 47N20

MathSciNet review:
1111439

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Abstract: Let be a closed, densely defined operator in a Hilbert space , and let , and be finite, scalar-valued measures on . Consider the abstract integrodifferential equation

**[1]**T. A. Burton and Bo Zhang,*Periodic solutions of finite- and infinite-dimensional functional-differential equations*, Finite- and infinite-dimensional dynamics (Kyoto, 1988) Lecture Notes Numer. Appl. Anal., vol. 15, Kinokuniya, Tokyo, 1996, pp. 1–19. MR**1470482****[2]**G. Gripenberg, S.-O. Londen, and O. Staffans,*Volterra integral and functional equations*, Encyclopedia of Mathematics and its Applications, vol. 34, Cambridge University Press, Cambridge, 1990. MR**1050319****[3]**A. Pazy,*Semigroups of linear operators and applications to partial differential equations*, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR**710486****[4]**Olof J. Staffans,*Some well-posed functional equations which generate semigroups*, J. Differential Equations**58**(1985), no. 2, 157–191. MR**794767**, 10.1016/0022-0396(85)90011-7**[5]**-,*Periodic solutions of an abstract integrodifferential equation*, Functional Differential Equations and Related Topics (Proc. Internat. Conf., Kyoto 1990), World Scientific, Singapore, 1991, pp. 344-348.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1993-1111439-X

Keywords:
Integrodifferential equation,
well-posedness,
periodic solutions,
-multipliers,
compact solution operator

Article copyright:
© Copyright 1993
American Mathematical Society