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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-1-3,
author = {Carlos Lizama and Rodrigo Ponce},
title = {Periodic solutions of degenerate differential equations in vector-valued function spaces},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {49-63},
zbl = {1219.35129},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-1-3}
}
Carlos Lizama; Rodrigo Ponce. Periodic solutions of degenerate differential equations in vector-valued function spaces. Studia Mathematica, Tome 204 (2011) pp. 49-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-1-3/