Title: R-boundedness Approach to linear third differential equations in a UMD Space,
Abstract: The aim of this work is to study the existence of a periodic solutions of
third order differential equations $z'''(t) = Az(t) + f(t)$ with the periodic
condition $x(0) = x(2\pi), x'(0) = x'(2\pi)$ and $x''(0) = x''(2\pi)$. Our
approach is based on the R-boundedness and $L^{p}$-multiplier of linear
operators.