Periodic solutions of an abstract third-order differential equation
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.