The fractional p(., .)-Neumann boundary conditions for the nonlocal p(., .)-Laplacian operator. Issue 3 (11th February 2023)

• Record Type: Journal Article
• Authors: Irzi, Nawal; Kefi, Khaled
• Is Part Of: Applicable analysis. Volume 102:Issue 3(2023)
• Page Start: 839
• Page End: 851
• Publication Date: 2023-02-11
• Subjects: Fractional p(..)-Laplacian -- p(..)-Neumann boundary condition -- Ekeland variational principle; 35D05 -- 35D30 -- 35J58 -- 35J60 -- 35J65; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1965585
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we deal with the fractional p ( ., . ) -Laplacian problem with nonlocal Neumann boundary conditions 1 { ( − Δ ) p ( ., . ) s u + | u | p ¯ ( x ) − 2 u = λ V 1 ( x ) | u | q ( x ) − 2 u, in Ω, N s, p ( ., . ) u = μ V 2 ( x ) | u | r ( x ) − 2 u, on R N ∖ Ω, here λ, μ > 0 are parameters and V 1, V 2 are two nonnegative weighted functions. The domain Ω ⊂ R N ( N ≥ 1 ) is smooth and bounded, p ¯ ( x ) = p ( x, x ), q, r are continuous bounded functions. Applying the Ekeland principle and the variational method, under appropriate assumptions, we show that the above problem has nontrivial weak solutions.