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

 

On a class of sublinear quasilinear elliptic problems


Author: D. D. Hai
Journal: Proc. Amer. Math. Soc. 131 (2003), 2409-2414
MSC (2000): Primary 35J25, 35J70
Published electronically: January 15, 2003
MathSciNet review: 1974638
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Abstract: We establish existence and multiplicity of positive solutions to the quasilinear boundary value problem

\begin{displaymath}\begin{split} \text{$div$ }(\vert\nabla u\vert^{p-2}\nabla u)... ...ega ,\\ u \ &= \ 0\text{ \ \ on }\partial \Omega , \end{split}\end{displaymath}

where $\Omega $ is a bounded domain in $R^{n}$ with smooth boundary $ \partial \Omega $, $f:[0,\infty )\rightarrow R$ is continuous and p-sublinear at $\infty ,$ and $\lambda $ is a large parameter.


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Additional Information

D. D. Hai
Affiliation: Department of Mathematics, Mississippi State University, Mississippi State, Mississippi 39762
Email: dang@ra.msstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06874-6
PII: S 0002-9939(03)06874-6
Keywords: Sub-supersolutions, quasilinear elliptic, positive solutions
Received by editor(s): March 7, 2002
Published electronically: January 15, 2003
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2003 American Mathematical Society