On the Behaviour of the First Eigenfunction of the p-Laplacian Near its Critical Points |
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Authors: | Garcia-Melian Jorge |
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Institution: | Departamento de Análisis Matemático, Universidad de La Laguna 38271 La Laguna, Tenerife (Spain) jjgarmel{at}ull.es |
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Abstract: | In this paper, the behaviour of the positive eigenfunction of in u| = 0, p > 1, isstudied near its critical points. Under some convexity and symmetryassumptions on , is seen to have a unique critical point atx = 0; also, the behaviour of both and is determined nearby.Positive solutions u to some general problems pu = f(u)in , u| = 0, are also considered, with some convexity restrictionson u. 2000 Mathematics Subject Classification 35B05 (primary),35J65, 35J70 (secondary). |
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