Fractional p-Laplacian equations on Riemannian manifolds
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Date
2018-08-22
Authors
Guo, Lifeng
Zhang, Binlin
Zhang, Yadong
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Fractional p-Laplacian, Riemannian manifolds, Variational methods
Citation
Guo, 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.
Rights
Attribution 4.0 International