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arXiv · 0708.1155

"Boundary blowup" type sub-solutions to semilinear elliptic equations with Hardy potential

Catherine Bandle·Vitaly Moroz·Wolfgang Reichel
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Abstract

Semilinear elliptic equations which give rise to solutions blowing up at the boundary are perturbed by a Hardy potential. The size of this potential effects 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. Our considerations are based on a Phragmen-Lindelof 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 sub- and super-solution techniques and on estimates for the Hardy constant derived in Marcus, Mizel and Pinchover.

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Catherine Bandle, Vitaly Moroz, Wolfgang Reichel. 2007-08-14. "Boundary blowup" type sub-solutions to semilinear elliptic equations with Hardy potential. https://doi.org/10.1112/jlms%2Fjdm104

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