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

 

Positive solutions of a degenerate elliptic equation with logistic reaction


Author: Shingo Takeuchi
Journal: Proc. Amer. Math. Soc. 129 (2001), 433-441
MSC (2000): Primary 35J70; Secondary 35B30
Published electronically: August 29, 2000
MathSciNet review: 1800233
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Abstract | References | Similar Articles | Additional Information

Abstract:

The degenerate elliptic equation $\lambda \Delta_p u +u^{q-1}(1-u^r)=0$ with zero Dirichlet boundary condition, where $\lambda$ is a positive parameter, $2<p<q$ and $r>0$, is studied in three aspects: existence of maximal solution, $\lambda$-dependence of maximal solution and multiplicity of solutions.


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Additional Information

Shingo Takeuchi
Affiliation: Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan
Email: stakeuchi@nyc.odn.ne.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05723-3
PII: S 0002-9939(00)05723-3
Keywords: $p$-Laplace operator, degenerate elliptic equation, flat hat, flat core, multiple solutions
Received by editor(s): April 15, 1999
Published electronically: August 29, 2000
Additional Notes: This work was partially supported by JSPS Research Fellowships for Japanese Young Scientists.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2000 American Mathematical Society