”boundary Blowup” Type Sub-solutions to Semilinear Elliptic Equations with Hardy Potential

Semilinear elliptic equations which give rise to solutions blowing up at the boundary are perturbed by a Hardy potential μ/δ(x, ∂Ω). The size of this potential effects the existence of a certain type of solutions (large solutions): if μ 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. Our considerations are based on a Phragmen-Lindelöf type theorem which enables us to classify the solutions and sub-solutions according to their behavior near the boundary. Nonexistence follows from this principle together with the Keller-Osserman upper bound. The existence proofs rely on suband super-solution techniques and on estimates for the Hardy constant derived in Marcus, Mizel and Pinchover [9].