Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/28572
Title: Positive solutions of elliptic equations with a strong singular potential
Contributor(s): Wei, Lei (author); Du, Yihong  (author)orcid 
Publication Date: 2019
Early Online Version: 2018-12-09
DOI: 10.1112/blms.12229
Handle Link: https://hdl.handle.net/1959.11/28572
Abstract: 

In this paper, we study positive solutions of the elliptic equation

−Δ=()−()inΩ,

where >2,>−, >1, ()=(,Ω), and Ω is a bounded smooth domain in ℝ(⩾2). When =2, the term 1()=1()2 is often called a Hardy potential, and the equation in this case has been extensively investigated. Here we consider the case >2, which gives a stronger singularity than the Hardy potential near Ω. We show that when <0, the equation has no positive solution, while when >0, the equation has a unique positive solution, and it satisfies

lim()→0()()+−1=1−1.

Publication Type: Journal Article
Grant Details: ARC/DP170103087
Source of Publication: Bulletin of the London Mathematical Society, 51(2), p. 251-266
Publisher: Wiley-Blackwell Publishing Ltd
Place of Publication: United Kingdom
ISSN: 1469-2120
0024-6093
Fields of Research (FoR) 2008: 010110 Partial Differential Equations
Fields of Research (FoR) 2020: 490410 Partial differential equations
Socio-Economic Objective (SEO) 2008: 970101 Expanding Knowledge in the Mathematical Sciences
Socio-Economic Objective (SEO) 2020: 280118 Expanding knowledge in the mathematical sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Appears in Collections:Journal Article
School of Science and Technology

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