The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators L p-multipliers and UMD-spaces.
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In this paper we give a necessary and suffcient conditions for the existence and uniqueness of periodic solutions of functional differential equations with n delay d dt x(t) = Ax(t) + n j=1 Bx(t − r j ) + f (t). The conditions are obtained in terms of R-boundedness of operator valued Fourier multipliers.
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