Fractional Sobolev spaces with kernel function on compact Riemannian manifoldsAberqi, Ahmed (Avtor) Ouaziz, Abdesslam (Avtor) Repovš, Dušan (Avtor) nonlinear elliptic problemfractional Sobolev spaceskernel functionLévy-integrability conditioncompact Riemannian manifoldsexistence of solutionstopological degree theoryIn this paper, a new class of Sobolev spaces with kernel function satisfying a Lévy-integrability-type condition on compact Riemannian manifolds is presented. We establish the properties of separability, reflexivity, and completeness. An embedding result is also proved. As an application, we prove the existence of solutions for a nonlocal elliptic problem involving the fractional $p(\cdot, \cdot)$-Laplacian operator. As one of the main tools, topological degree theory is applied.20242023-11-27 10:02:45Članek v reviji152540sl