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.