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