An n-dimensional pendulum-like equation via topological methods

We study the elliptic boundary value problem Δu+g(u)=p(x) with nonlinear periodic-type boundary conditions. We prove the existence of a solution under a Landesman-Lazer-type condition. Moreover, using the method of upper and lower solutions we study a problem which concerns the range of the semilinear operator Su=Δu+g(u).