In this work we study the problem
in the unit ball of , with on the boundary, where , and is a real parameter. We assume that the nonlinearity has a zero of order . Our main contribution is showing that there exists a unique positive solution of this problem for large enough and maximum close to . This will be achieved by means of a linearization technique, and we also prove the new result that the inverse of the -Laplacian is differentiable around positive solutions.
Submitted July 5, 2004. Published September 21, 2004.
Math Subject Classifications: 35J60, 35J70.
Key Words: p-Laplacian; linearization; uniqueness
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| Jorge Garcia-Melian |
Dpto. de Analisis Matematico
Universidad de La Laguna
38271 La Laguna - Tenerife, Spain
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