Eigenvalue type problem in s(.,.)-fractional Musielak-Sobolev spaces

2023/01/01 by E. Azroul, Azroul, E., A. Benkirane +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2301.00467

openalex publication_date 2023/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, first we introduce the s(.,.)-fractional Musielak-Sobolev spaces W^s(x,y)L_\varPhi_x,y(Ω). Next, by means of Ekeland's variational principal, we show that there exists λ_*>0 such that any λ∈(0, λ_*) is an eigenvalue for the following problem (P_a) \ ( -Δ)^s(x,.)_a_(x,.) u = λ|u|^q(x)-2u · amp; \rm in Ω,
u = 0 · amp; \rm in ℝ^N∖ Ω, . where Ω is a bounded open subset of ℝ^N with C^0,1-regularity and bounded boundary.

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