Periodic solutions of degenerate differential equations in vector-valued function spaces
Volume 202 / 2011
Studia Mathematica 202 (2011), 49-63
MSC: Primary 35K65; Secondary 34G10, 34K13.
DOI: 10.4064/sm202-1-3
Abstract
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 $\frac{d}{dt}(Mu(t)) = Au(t) + f(t)$, 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.
