Using operator valued Fourier multipliers, we characterize maximal regularity for the abstract third-order differential equation αu'''(t) + u''(t) = βAu(t) + γBu'(t) + f(t) with boundary conditions u(0) = u(2π), u'(0) = u'(2π) and u''(0) = u''(2π), where A and B are closed linear operators defined on a Banach space X, α,β,γ ∈ ℝ₊, and f belongs to either periodic Lebesgue spaces, or periodic Besov spaces, or periodic Triebel-Lizorkin spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-3-1,
author = {Ver\'onica Poblete and Juan C. Pozo},
title = {Periodic solutions of an abstract third-order differential equation},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {195-219},
zbl = {1281.34107},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-3-1}
}
Verónica Poblete; Juan C. Pozo. Periodic solutions of an abstract third-order differential equation. Studia Mathematica, Tome 215 (2013) pp. 195-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-3-1/