Existence, regularity and stability properties of periodic solutions of a capillarity equation in the presence of lower and upper solutions

We develop a lower and upper solutions method for the periodic problem associated with the capillarity equation −(u′/1+u′2)′=f(t,u) in the space of bounded variation functions. We get the existence of periodic solutions both in the case where the lower solution αα and the upper solution ββ satisfy α≤βα≤β, and in the case where α≰βα≰β. In the former case we also prove regularity and order stability of the solutions.