On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding

Abdelouahed El Khalil; Mohammed Ouanan

Applicationes Mathematicae, Tome 32 (2005), p. 1-16 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that for any λ ∈ ℝ, there is an increasing sequence of eigenvalues μₙ(λ) for the nonlinear boundary value problem ⎧ $Δ ₚ u = {| u |}^{p - 2} u$ in Ω, ⎨ ⎩ ${| \nabla u |}^{p - 2} \partial u / \partial ν = {λ ϱ (x) | u |}^{p - 2} u + μ {| u |}^{p - 2} u$ on crtial ∂Ω and we show that the first one μ₁(λ) is simple and isolated; we also prove some results about variations of the density ϱ and the continuity with respect to the parameter λ.

Publié le : 2005-01-01

Zbl 1080.35056

EUDML-ID : urn:eudml:doc:286082

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     author = {Abdelouahed El Khalil and Mohammed Ouanan},
     title = {On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding},
     journal = {Applicationes Mathematicae},
     volume = {32},
     year = {2005},
     pages = {1-16},
     zbl = {1080.35056},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-1-1}
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Abdelouahed El Khalil; Mohammed Ouanan. On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding. Applicationes Mathematicae, Tome 32 (2005) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-1-1/