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

Abdelouahed El Khalil, and Mohammed Ouanan. "On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding." Applicationes Mathematicae 32.1 (2005): 1-16. <http://eudml.org/doc/286082>.

@article{AbdelouahedElKhalil2005,
abstract = {We prove that for any λ ∈ ℝ, there is an increasing sequence of eigenvalues μₙ(λ) for the nonlinear boundary value problem ⎧ $Δₚu = |u|^\{p-2\}u$ in Ω, ⎨ ⎩ $|∇u|^\{p-2\} ∂u/∂ν = λϱ(x)|u|^\{p-2\}u + μ|u|^\{p-2\}u$ 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.},
author = {Abdelouahed El Khalil, Mohammed Ouanan},
journal = {Applicationes Mathematicae},
keywords = {nonlinear eigenvalue problem; nonlinear boundary conditions; principal eigenfunction; first eigenvalue},
language = {eng},
number = {1},
pages = {1-16},
title = {On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding},
url = {http://eudml.org/doc/286082},
volume = {32},
year = {2005},
}

TY - JOUR
AU - Abdelouahed El Khalil
AU - Mohammed Ouanan
TI - On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding
JO - Applicationes Mathematicae
PY - 2005
VL - 32
IS - 1
SP - 1
EP - 16
AB - We prove that for any λ ∈ ℝ, there is an increasing sequence of eigenvalues μₙ(λ) for the nonlinear boundary value problem ⎧ $Δₚu = |u|^{p-2}u$ in Ω, ⎨ ⎩ $|∇u|^{p-2} ∂u/∂ν = λϱ(x)|u|^{p-2}u + μ|u|^{p-2}u$ 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.
LA - eng
KW - nonlinear eigenvalue problem; nonlinear boundary conditions; principal eigenfunction; first eigenvalue
UR - http://eudml.org/doc/286082
ER -