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We are concerned with the existence of almost automorphic mild solutions to the perturbed abstract differential equations of the form x(t) = (A + B)x(t) (*), where A is a unbounded linear operator generator of a Co-group of bounded operators and B is a bounded linear operator acting in a Banach space X. Under suitable conditions we show that every bounded mild solution to (*) is almost automorphic. Meanwhile under a relatively compactness hypothesis of the range of a solution, we show that such a solution is also almost periodic.
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Rocznik
Tom
Strony
201--206
Opis fizyczny
Bibliogr. 4 poz.
Twórcy
autor
- Department of Mathematics, Howard University, 2441 6th Street N.W. Wasington D.C. 20059, USA
autor
- Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA
Bibliografia
- [1] J. A. Goldstein, Convexity, Boundedness and almost periodicity for differential equations in Hilbert Spaces, Int. J. Math and Math, Sci., 2 (1979), 1-13.
- [2] G. M. N’Guerekata, Almost automorphic functions and applications to abstract euolution equations, Cont. Math. AMS 252 (1999), 71-76.
- [3] G. M. N’Guerekata, Almost Automorphic Functions and Almost Periodic Functions in Abstract Spaces, Kluwer Academic/ Publisher, New York, 2001.
- [4] A. M. Fink, Almost Periodic Differential Equations, Lecture Notes in Mathematics 337, Springer-Verlag, Berlin-Heidelberg-New York (1974).
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Bibliografia
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bwmeta1.element.baztech-article-BUS2-0002-0074