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

• Autorzy: Abdelouahed El Khalil , Mohammed Ouanan
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35J20: Variational methods for second-order elliptic equations
• 35J60: Nonlinear elliptic equations
• 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2005
• Tom: 32
• Numer: 1
• Strony: 1-16

Daty

wydano

2005

Twórcy

autor

Abdelouahed El Khalil

• Département de Mathématiques & Génie Industriel, École Polytechnique, Montréal, Montréal (QC) H3C 3A7, Canada

autor

Mohammed Ouanan

• Departement of Mathematics, Faculty of Sciences Dhar-Mahraz, P.O. Box 1796, Atlas, Fez 30000, Morocco

Identyfikatory

DOI

10.4064/am32-1-1