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Bifurcation for some quasilinear operators

Published online by Cambridge University Press:  12 July 2007

David Arcoya ,
José Carmona  and
Benedetta Pellacci
David Arcoya
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, C/Ochoa, 18071 Granada, Spain (darcoya@ugr.es)
José Carmona
Affiliation:
Departamento de Álgebra y Análisis Matemático, Facultad de Ciencias, Cañada de San Urbano, Almeria, Spain (jcarmona@ual.es)
Benedetta Pellacci
Affiliation:
Scuola Normale Superiore, Piazza Dei Cavalieri 7, 56126 Pisa, Italy (pellacci@cibs.sns.it)
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Abstract

This paper deals with existence, uniqueness and multiplicity results of positive solutions for the quasilinear elliptic boundary-value problem , where Ω is a bounded open domain in RN with smooth boundary. Under suitable assumptions on the matrix A(x, s), and depending on the behaviour of the function f near u = 0 and near u = +∞, we can use bifurcation theory in order to give a quite complete analysis on the set of positive solutions. We will generalize in different directions some of the results in the papers by Ambrosetti et al., Ambrosetti and Hess, and Artola and Boccardo.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 4 , August 2001 , pp. 733 - 765
Copyright
Copyright © Royal Society of Edinburgh 2001

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