Existence of solution for a system involving a singular-nonlocal operator, a singularity and a Radon measure. Issue 4 (3rd April 2022) - Soni, Amita; Datta, Sanjoy; Saoudi, K.; Choudhuri, D.
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.