  In the first part of the article, we give necessary and sufficient conditions
for the solvability of a class of nonlinear elliptic boundary value problems
with nonlinear boundary conditions involving the q-Laplace-Beltrami operator.
In the second part, we give some additional results on existence, uniqueness
and continuous dependence estimates of the weak solutions for these classes of
nonlinear problems. Finally, we show that these solutions are also bounded and
provide explicit estimates.
