Simplicity and stability of the first eigenvalue of a nonlinear elliptic system

Abdelouahed El Khalil, Said El Manouni and Mohammed Ouanan

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-9

Abstract:

We prove some properties of the first eigenvalue for the elliptic system − Δ p u = λ | u | α | v | β v in Ω , − Δ q v = λ | u | α | v | β u in Ω , ( u , v ) ∈ W 0 1 , p ( Ω ) × W 0 1 , q ( Ω ) . In particular, the first eigenvalue is shown to be simple. Moreover, the stability with respect to ( p , q ) is established.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:328340

DOI: 10.1155/IJMMS.2005.1555

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