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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Stability and instability of positive solutions of semipositone problems


Author: Achilles Tertikas
Journal: Proc. Amer. Math. Soc. 114 (1992), 1035-1040
MSC: Primary 35B35; Secondary 35J65
MathSciNet review: 1092928
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Abstract: We consider the boundary value problem

$\displaystyle - \Delta u = f(u)\,{\text{in}}\,\Omega {\text{,}}Bu = 0\,{\text{on}}\,\partial \Omega ,$

where $ \Omega $ is a bounded region in $ {\mathbb{R}^n}$ with smooth boundary. We prove stability and instability results of positive solutions under various choices of $ f$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1092928-2
PII: S 0002-9939(1992)1092928-2
Keywords: Subsupersolutions, linearized stability, positone
Article copyright: © Copyright 1992 American Mathematical Society