We study the boundary blow-up elliptic problem in a smooth bounded domain , with . Under suitable growth assumptions on near and on both at zero and at infinity, we prove the existence of at least a positive solution. Our proof is based on the method of sub and supersolutions, which permits on the one hand oscillatory behaviour of at infinity and on the other hand positive weights which are unbounded and/or oscillatory near the boundary.
Submitted July 4, 2003. Published November 4, 2003.
Math Subject Classifications: 35J60, 35J25.
Key Words: Boundary blow-up, sub and supersolutions
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|Jorge Garcia-Melian |
Dpto. de Analisis Matematico, Universidad de La Laguna
c. Astrofisico Francisco Sanchez s/n, 38271 - La Laguna, Spain
Centro de Modelamiento Matematico, Universidad de Chile
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