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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 the equation $ {\rm div}\,(\vert \nabla u\vert \sp {p-2}\nabla u)+\lambda\vert u\vert \sp {p-2}u=0$


Author: Peter Lindqvist
Journal: Proc. Amer. Math. Soc. 109 (1990), 157-164
MSC: Primary 35J60; Secondary 35P05
Addendum: Proc. Amer. Math. Soc. 116 (1992), 583-584.
MathSciNet review: 1007505
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Abstract: The first eigenvalue $ \lambda = {\lambda _1}$ for the equation $ \operatorname{div} ({\text{\vert}}\nabla u{{\text{\vert}}^{p - 2}}\nabla u{\text{) + }}\lambda {\text{\vert}}u{{\text{\vert}}^{p - 2}}u = 0$ is simple in any bounded domain. (Through the nonlinear counterpart to the Rayleigh quotient $ {\lambda _1}$ is related to the Poincaré inequality.)


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1007505-7
PII: S 0002-9939(1990)1007505-7
Article copyright: © Copyright 1990 American Mathematical Society