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

摘要

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 α and the upper solution β satisfy α≤β, and in the case where α?β. In the former case we also prove regularity and order stability of the solutions.