Periodic solutions of an abstract third-order differential equation
Volume 215 / 2013
Studia Mathematica 215 (2013), 195-219
MSC: Primary 34G10; Secondary 34C25.
DOI: 10.4064/sm215-3-1
Abstract
Using operator valued Fourier multipliers, we characterize maximal regularity for the abstract third-order differential equation $\alpha u'''(t) + u''(t) = \beta Au(t) +\gamma Bu'(t) +f(t)$ with boundary conditions $u(0)=u(2\pi )$, $u'(0)=u'(2\pi )$ and $u''(0)=u''(2\pi )$, where $A$ and $B$ are closed linear operators defined on a Banach space $X$, $\alpha ,\beta ,\gamma \in \mathbb {R}_+$, and $f$ belongs to either periodic Lebesgue spaces, or periodic Besov spaces, or periodic Triebel–Lizorkin spaces.
