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

Abstract

We develop a lower and upper solutions method for the periodic problem associated with the capillarity equation − “ u/ p 1 + u′ ”′ = 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 6≤ β. In the former case we also prove regularity and order stability of solutions. 2010 Mathematics Subject Classification: 34C25, 34B15, 76D45, 47H07, 34D20, 49Q20.

Cite this paper

@inproceedings{Obersnel2012ExistenceRA, title={Existence, regularity and stability properties of periodic solutions of a capillarity equation in the presence of lower and upper solutions}, author={Franco Obersnel and Pierpaolo Omari and Sabrina Rivetti}, year={2012} }