can anyone recommend good books and/or articles for the mathematical analysis of periodic solutions of a PDE, for example something like
$$u(t)-u''(t)=f(t) $$ with $u(0)=u(1)$ and $u'(0)=u'(1)$ ?
Something that treats the weak formulations, regularity... etc.
I'm good with googling things but so far nothing of note has popped up, and the wikipedia article doesn't really give me what I'm looking for. Thanks !