Existence of solution for a system involving a singular-nonlocal operator, a singularity and a Radon measure. Issue 4 (3rd April 2022)

• Record Type: Journal Article
• Authors: Soni, Amita; Datta, Sanjoy; Saoudi, K.; Choudhuri, D.
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 4(2022)
• Page Start: 872
• Page End: 886
• Publication Date: 2022-04-03
• Subjects: X. Xie; Marcinkiewicz space -- capacity -- subdifferential -- Radon measure; 35J35 -- 35J60; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1849157
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : The existence of a nontrivial solution in some 'weaker' sense of the system of equations: 1 L s u + l ( x ) ϕ u + w ( x ) u k = μ i n Ω, ( − Δ ) s ϕ = l ( x ) u 2 i n Ω, u > 0 i n Ω, u = ϕ = 0 i n R N ∖ Ω is proved. Here, L s u = ( − Δ ) s u − λ u − β, λ > 0, 0 < β ≤ s < 1, l, w are bounded, nonnegative real-valued functions in Ω, μ is a nonnegative Radon measure and k >1 belongs to a certain range.