Let $g:R \rightarrow R$ be continuous and $ 2\pi$-periodic, let $m \in N$. How many solution in class of $m$-times continuously differentiable $2\pi$-periodic functions has equation $f^{(m)}=g ?$
Edit. Obviously, if $f$ is a solution in this class and $C$ is a constant then $f+C$ is also a solution. Are there another solutions?