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Proceedings of the American Mathematical Society

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

 

 

On a singular nonlinear elliptic boundary-value problem


Authors: A. C. Lazer and P. J. McKenna
Journal: Proc. Amer. Math. Soc. 111 (1991), 721-730
MSC: Primary 35J60; Secondary 35B65
DOI: https://doi.org/10.1090/S0002-9939-1991-1037213-9
MathSciNet review: 1037213
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Abstract: We consider the singular boundary-value problem $ \Delta u + p(x){u^{ - \gamma }} = 0$ in $ \Omega ,u\vert\partial \Omega = 0$, where $ \gamma > 0$. Under the assumption $ p(x) > 0$ and certain smoothness assumptions, we show that there exists a solution which is smooth on $ \Omega $ and continuous on $ \bar \Omega $.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1037213-9
Keywords: Eigenfunction, subsolution, supersolution
Article copyright: © Copyright 1991 American Mathematical Society