On a class of nonlocal problems in new fractional Musielak-Sobolev spaces. Issue 6 (13th April 2022) - Azroul, E.; Benkirane, A.; Shimi, M.; Srati, M.
ABSTRACT: In this paper, we first introduce the new fractional Musielak-Sobolev spaces, and we establish some qualitative properties of these spaces. Then, using the direct variational approach, we investigate the existence of a nontrivial weak solution for a class of fractional type problems with Dirichlet boundary data of the following form 1 ( P a ) ( − Δ ) a ( x, . ) s u + a ˆ x ( | u | ) u = f ( x, u ) in Ω, u = 0 in R N ∖ Ω, where s ∈ ( 0, 1 ), Ω is an open bounded subset in R N with Lipschitz boundary ∂ Ω, and f : Ω × R ⟶ R is a Carathéodory function with suitable growth conditions.