The Solvability of Fractional Elliptic Equation with the Hardy Potential. (28th May 2020)

• Record Type: Journal Article
• Authors: Gao, Siyu; Huang, Shuibo; Tian, Qiaoyu; Ma, Zhan-Ping
• Other Names: Li Chun-Lai Guest Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-05-28
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/5414309
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : In this paper, we study the existence and nonexistence of solutions to fractional elliptic equations with the Hardy potential − Δ s u − λ u / x 2 s = u r − 1 + δ g u, in Ω, u x > 0, in Ω, u x = 0, in ℝ N ∖ Ω, where Ω ⊂ ℝ N is a bounded Lipschitz domain with 0 ∈ Ω, − Δ s is a fractional Laplace operator, s ∈ 0, 1, N > 2 s, δ is a positive number, 2 < r < r λ, s ≡ N + 2 s − 2 α λ / N − 2 s − 2 α λ + 1, α λ ∈ 0, N − 2 s / 2 is a parameter depending on λ, 0 < λ < Λ N, s, and Λ N, s = 2 2 s Γ 2 N + 2 s / 4 / Γ 2 N − 2 s / 4 is the sharp constant of the Hardy–Sobolev inequality.