Semilinear elliptic equations which give rise to solutions blowing up at the
boundary are perturbed by a Hardy potential involving distance to the boundary.
The size of this potential affects the existence of a certain type of solutions
(large solutions): if the potential is too small, then no large solution exists.
The presence of the Hardy potential requires a new definition of large solutions,
following the pattern of the associated linear problem. Nonexistence and existence
results for different types of solutions will be given. Considerations are based
on a Phragmen-Lindelof type theorem which enables to classify the solutions and
sub-solutions according to their behavior near the boundary and on Hardy constant
estimates derived by Marcus, Mizel and Pinchover.