Fractional p-Laplacian equations on Riemannian manifolds
| dc.contributor.author | Guo, Lifeng | |
| dc.contributor.author | Zhang, Binlin | |
| dc.contributor.author | Zhang, Yadong | |
| dc.date.accessioned | 2022-02-22T20:58:34Z | |
| dc.date.available | 2022-02-22T20:58:34Z | |
| dc.date.issued | 2018-08-22 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15405 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional p-Laplacian | |
| dc.subject | Riemannian manifolds | |
| dc.subject | Variational methods | |
| dc.title | Fractional p-Laplacian equations on Riemannian manifolds | en_US |
| dc.type | Article |