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Global branches of positive weak solutions of semilinear elliptic problems over nonsmooth domains

Published online by Cambridge University Press:  14 November 2011

Timothy J. Healey ,
Hansjörg Kielhöfer  and
Charles A. Stuart
Timothy J. Healey
Affiliation:
Department of Theoretical & Applied Mechanics and Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, U.S.A.
Hansjörg Kielhöfer
Affiliation:
Institut für Mathematik, Universität Augsburg, Universitätsstraße 8, D-8900 Augsburg, Germany
Charles A. Stuart
Affiliation:
Départment de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
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Abstract

We consider the nonlinear eigenvalue problem posed by a parameter-dependent semilinear second-order elliptic equation on a bounded domain with the Dirichlet boundary condition. The coefficients of the elliptic operator are bounded measurable functions and the boundary of the domain is only required to be regular in the sense of Wiener. The main results establish the existence of an unbounded branch of positive weak solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 2 , 1994 , pp. 371 - 388
Copyright
Copyright © Royal Society of Edinburgh 1994

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