Existence of Solutions to the Second Boundary-Value Problem for the $p$-Laplacian on Riemannian Manifolds

We obtain necessary and sufficient conditions for the existence of solutions to the boundary-value problem
$$ \Delta_p u=f\quad\text{on}\quad M,\qquad |\nabla u|^{p-2}\,\frac {\partial u}{\partial \nu}\bigg|_{\partial M}=h, $$
where $p > 1$ is a real number, $M$ is a connected oriented complete Riemannian manifold with boundary, and $\nu$ is the outer normal vector to $\partial M$.