# On the Equation $\operatorname{div}(|\nabla u|^{p-2}\nabla u) + \lambda|u| ^{p-2}u = 0$

Peter Lindqvist
Proceedings of the American Mathematical Society
Vol. 109, No. 1 (May, 1990), pp. 157-164
DOI: 10.2307/2048375
Stable URL: http://www.jstor.org/stable/2048375
Page Count: 8

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## Abstract

The first eigenvalue λ = λ1 for the equation $\operatorname{div}(|\nabla u|^{p - 2}\nabla u) + \lambda|u|^{p - 2}u = 0$ is simple in any bounded domain. (Through the nonlinear counterpart to the Rayleigh quotient λ1 is related to the Poincare inequality.)

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