On some perturbations of some abstract differential equations

• Autorzy: Diagana T. , Nguerekata G. M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

almost automorphic function; almost periodic functions; mild solution

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2003
• Tom: [Z] 43(2)
• Strony: 201--206
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Diagana T.

• Department of Mathematics, Howard University, 2441 6th Street N.W. Wasington D.C. 20059, USA

autor

Nguerekata G. M.

• 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).