On the Eigenvalues of the p&q- Fractional Laplacian

2023/02/22 by Sabri Bahrouni, Bahrouni, Sabri, Hichem Hajaiej +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2302.11473

openalex publication_date 2023/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the eigenvalue problem for the fractional p & q-Laplacian \\beginaligned (- Δ)_p^s u + μ(- Δ)_q^s u+ |u|^p-2u+μ|u|^q-2u=λ V(x)|u|^p-2u amp; in Ω
u=0\quadamp; in \R^N\backslashΩ, \endaligned. where Ω is an open bounded, and possibly disconnected domain, λ∈\R, 10 with a weight function in L^∞(Ω) that is allowed no change sign. We show that the problem has a continuous spectrum. Moreover, our result reveals a discontinuity property for the spectrum as the parameter μ→ 0⁺. In addition, a stability property of eigenvalues as s→ 1^- is established.

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