A singular elliptic problem involving fractional p-Laplacian and a discontinuous critical nonlinearity

The purpose of this article is to prove the existence of solution to a nonlinear nonlocal elliptic problem with a singularity and a discontinuous critical nonlinearity, which is given as (−Δ)psu= μg(x,u)+λuγ+H(u−α)ups*−1inΩ,u>0inΩ, with the zero Dirichlet boundary condition. Here, Ω⊂RN is a bound...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-07, Vol.62 (7)
Main Authors: Saoudi, Kamel, Panda, Akasmika, Choudhuri, Debajyoti
Format: Article
Language:English
Subjects:
Boundary conditions
Dirichlet problem
Nonlinearity
Physics
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Summary:The purpose of this article is to prove the existence of solution to a nonlinear nonlocal elliptic problem with a singularity and a discontinuous critical nonlinearity, which is given as (−Δ)psu= μg(x,u)+λuγ+H(u−α)ups*−1inΩ,u>0inΩ, with the zero Dirichlet boundary condition. Here, Ω⊂RN is a bounded domain with Lipschitz boundary, s ∈ (0, 1), 2 0. Under suitable assumptions on the function g, the existence of solution to the problem has been established. Furthermore, it will be shown that as α → 0+, the sequence of solutions of the problem for each such α converges to a solution of the problem for which α = 0.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0037375