where the second order differential operator F is of Hamilton-Jacobi-Bellman (HJB) type, that is, F is a supremum of linear elliptic operators, f is sublinear in u at infinity, and Ω ⊂ R is a regular bounded domain. HJB operators have been the object of intensive study during the last thirty years – for a general review of their theory and applications we refer to [26], [33], [43], [14]. Well-k...

In this paper we consider two elliptic problems. The first one is a Dirichlet problem while the second is Neumann. We extend all the known results concerning Landesman-Laser conditions by using the Mountain-Pass theorem with the Cerami (PS) condition.

We prove a saddle point theorem for locally Lipschitz functionals with arguments based on a version of the mountain pass theorem for such kind of functionals. This abstract result is applied to solve two diierent types of multivalued semilinear elliptic boundary value problems with a Laplace{Beltrami operator on a smooth compact Riemannian manifold. The mountain pass theorem of Ambrosetti and R...