Guo, LifengZhang, BinlinZhang, Yadong2022-02-222022-02-222018-08-22Guo, L., Zhang, B., & Zhang, Y. (2018). Fractional p-Laplacian equations on Riemannian manifolds. <i>Electronic Journal of Differential Equations, 2018</i>(156), pp. 1-17.1072-6691https://hdl.handle.net/10877/15405In this article we establish the theory of fractional Sobolev spaces on Riemannian manifolds. As a consequence we investigate some important properties, such as the reflexivity, separability, the embedding theorem and so on. As an application, we consider fractional p-Laplacian equations with homogeneous Dirichlet boundary conditions (-∆g)spu(x) = ƒ(x, u) in Ω, u = 0 in M \ Ω, where N > ps with s ∈ (0, 1), p ∈ (1, ∞), (-∆g)sp is the fractional p-Laplacian on Riemannian manifolds, (M, g) is a compact Riemannian N-manifold, Ω is an open bounded subset of M with smooth boundary ∂Ω, and ƒ is a Carathéodory function satisfying the Ambrosetti-Rabinowitz type condition. By using variational methods, we obtain the existence of nontrivial weak solutions when the nonlinearity ƒ satisfies sub-linear or super-linear growth conditions.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalFractional p-LaplacianRiemannian manifoldsVariational methodsArticle