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Vietnam Journal of Mathematics 33:1 (2005) 63-72

Almost Periodic Solutions of Evolution Equations

Associated with C-Semigroups:

An Approach Via Implicit Difference Equations

Nguyen Minh Man

Abstract. The paper is concerned with the existence of almost periodic mild solutions to evolution equations of the form ů(t)= Au(t) + f(t) (), where A generates a C-semigroup and f  is almost periodic. We investigate the existence of almost periodic solutions of () by means of associated implicit difference equations which are well-studied in recent works on the subject. As results we obtain various sufficient conditions for the existence of almost periodic solutions to () which extend previous ones to a more general class of ill-posed equations involving C-semigroups. The paper is supported by a research grant of the Vietnam National University, Hanoi.

 

 

 

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