Periodic solutions of an abstract third-order differential equation

Abstract

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, pha;, β, γ G R+, and f belongs to either periodic Lebesgue spaces, or periodic Besov spaces, or periodic Triebel-Lizorkin spaces. © Instytut Matematyczny PAN, 2013.