On the equation ๐‘‘๐‘–๐‘ฃ(|โˆ‡๐‘ข|^{๐‘-2}โˆ‡๐‘ข)+๐œ†|๐‘ข|^{๐‘-2}๐‘ข=0

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Abstract
The first eigenvalue <!-- MATH $\lambda = {\lambda _1}$ --> for the equation <!-- MATH $\operatorname{div} ({\text{|}}\nabla u{{\text{|}}^{p - 2}}\nabla u{\text{) + }}\lambda {\text{|}}u{{\text{|}}^{p - 2}}u = 0$ --> is simple in any bounded domain. (Through the nonlinear counterpart to the Rayleigh quotient <!-- MATH ${\lambda _1}$ --> is related to the Poincaré inequality.)

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