  We present a nonvariational setting for the Neumann problem for the Poisson
equation for solutions that are H\"{o}lder continuous and that may have
infinite Dirichlet integral. We introduce a distributional normal derivative on
the boundary for the solutions that extends that for harmonic functions that
has been introduced in a previous paper and we solve the nonvariational Neumann
problem for data in the interior with a negative Schauder exponent and for data
on the boundary that belong to a certain space of distributions on the
boundary.
