Displaying similar documents to “Periodical solutions of some differential equations with small parameter”

Periodic solutions of degenerate differential equations in vector-valued function spaces

Carlos Lizama, Rodrigo Ponce (2011)

Studia Mathematica

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Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces. ...