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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On positive solutions of semilinear elliptic equations


Authors: E. N. Dancer and Klaus Schmitt
Journal: Proc. Amer. Math. Soc. 101 (1987), 445-452
MSC: Primary 35B05; Secondary 35J65
DOI: https://doi.org/10.1090/S0002-9939-1987-0908646-2
MathSciNet review: 908646
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Abstract: This paper is concerned with necessary conditions for the existence of positive solutions of the semilinear problem $ \Delta u + f(u) = 0,x \in \Omega ,u = 0,x \in \partial \Omega $, whose supremum norm bears a certain relationship to zeros of the nonlinearity $ f$. We first discuss the smooth case (i.e., $ f$ and $ \partial \Omega $ smooth) and then show how to obtain similar results in the nonsmooth case.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0908646-2
Article copyright: © Copyright 1987 American Mathematical Society