Multiple bounded variation solutions of a capillarity problem

Abstract

We discuss existence and multiplicity of bounded variation solutions of the non-homogeneous Neumann problem for the prescribed mean curvature equation -div$(\nabla u/\sqrt(1+|\nablau|^2))=g(x,u)+h$ in $\Omega$ -$\nablau*v/\sqrt(1+|\nablau|^2)=k$ on $\partial\Omega$ where $g(x, s)$ is periodic with respect to $s$. Our approach is variational and makes use of non-smooth critical point theory in the space of bounded variation functions.