On a Study of Generalized Choquard-Logarithmic Problem in Fractional Musielak Spaces

We study a nonlocal Choquard-logarithmic problem in the setting of fractional Musielak-Sobolev spaces, a recently introduced framework by Sousa et al. The Choquard nonlinearity is expressed in terms of a Jacobian determinant, a novel formulation that enhances the problem’s generality and unifies several existing models in the literature. By employing variational methods, Ekeland’s variational principle, and a newly established version of the Hardy-Littlewood-Sobolev inequality (proved in this work), we prove the existence and multiplicity of solutions for this problem.