  Let (M,g) be a smooth connected compact Riemannian manifold of finite
dimension n \geq 2 with a smooth boundary \partial M. We consider the problem
-{\epsilon}^2\Delta_gu+u=|u|^{p-2}u, u>0 on M, \partial u/ \partial{\nu}=0 on
\partial M where {\nu} is an exterior normal to \partial M. The number of
solutions of this problem depends on the topological properties of the
manifold. In particular we consider the Lusternik Schnirelmann category of the
boundary.
