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

Abdelouahed El Khalil;  Mohammed Ouanan — 2005

Applicationes Mathematicae

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, ⎨ ⎩ | ∇ u | p - 2 ∂ u / ∂ 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.

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