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.identifier.citation | Guo, L., Zhang, B., & Zhang, Y. (2018). Fractional p-Laplacian equations on Riemannian manifolds. Electronic Journal of Differential Equations, 2018(156), pp. 1-17. | en_US |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://digital.library.txstate.edu/handle/10877/15405 | |
| 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, 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.language.iso | en | en_US |
| dc.publisher | Texas State University, Department of Mathematics | en_US |
| dc.subject | Fractional p-Laplacian | en_US |
| dc.subject | Riemannian manifolds | en_US |
| dc.subject | Variational methods | en_US |
| dc.title | Fractional p-Laplacian equations on Riemannian manifolds | en_US |
