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

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Lizama C., Ponce R.

Studia Mathematica

2011

tom 202

nr 1

49-63

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.

Ograniczanie wyników

1 Studia Mathematica

1 Lizama C.

1 Ponce R.

1 2011

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