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A global branch of positive solutions above the continuous spectrum for problems with indefinite nonlinearities

Published online by Cambridge University Press:  14 November 2011

Tassilo Küpper  and
Achilles Tertikas
Tassilo Küpper
Affiliation:
Institute of Mathematics, University of Cologne, Weyertal 86–90, D-50931 Köln, Germany
Achilles Tertikas
Affiliation:
Department of Mathematics, University of Crete, P.O. Box 1470, Iraklion, Crete, Greece
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Extract

We prove the existence and bifurcation of a global branch of positive solutions for a nonlinear Neumann eigenvalue problem on the half axis [0, ∞). The nonlinearity is assumed to have a superlinear growth multiplied by a weight function changing sign. This leads to the existence of nontrivial solutions above the continuous spectrum of the linearised problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 3 , 1996 , pp. 465 - 482
Copyright
Copyright © Royal Society of Edinburgh 1996

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