averaging; singularly perturbed equations on tori; Banach fixed point theorem
The existence of classical solutions for some partial differential equations on tori is shown.
 T. Kato: Locally coercive nonlinear equations, with applications to some periodic solutions
. Duke Math. Journal 51 (1984), 923-936. MR 0771388
| Zbl 0571.47051
 J. Moser: A rapidly convergent iteration method and nonlinear partial differential equations, I. Ann. Scuola Norm. Sup. Pisa 20(1966), 226-315.