Please use this identifier to cite or link to this item:
https://hdl.handle.net/1959.11/7471
Title: | Isolated singularities for weighted quasilinear elliptic equations | Contributor(s): | Cirstea, Florica C (author); Du, Yihong (author) | Publication Date: | 2010 | DOI: | 10.1016/j.jfa.2010.03.015 | Handle Link: | https://hdl.handle.net/1959.11/7471 | Abstract: | We classify all the possible asymptotic behavior at the origin for positive solutions of quasilinear elliptic equations of the form div(∇|u|ᵖ⁻²∇u)=b(x)h(u) in Ω∖{0}, where 1∠p≤N and Ω is an open subset of ℝᴺ with 0∈Ω. Our main result provides a sharp extension of a well-known theorem of Friedman and Véron for h(u)=uq and b(x)≡1, and a recent result of the authors for p=2 and b(x)≡1. We assume that the function h is regularly varying at ∞ with index q (that is, limt→∞h(λt)/h(t)=λq for every λ>0) and the weight function b(x) behaves near the origin as a function b0(|x|) varying regularly at zero with index θ greater than −p. This condition includes b(x)=|x|θ and some of its perturbations, for instance, b(x)=|x|θ(−log|x|)ͫ for any m ∈ ℝ. Our approach makes use of the theory of regular variation and a new perturbation method for constructing sub- and super-solutions. | Publication Type: | Journal Article | Source of Publication: | Journal of Functional Analysis, 259(1), p. 174-202 | Publisher: | Elsevier Inc | Place of Publication: | United States of America | ISSN: | 1096-0783 0022-1236 |
Fields of Research (FoR) 2008: | 010110 Partial Differential Equations | Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
---|---|
Appears in Collections: | Journal Article |
Files in This Item:
File | Description | Size | Format |
---|
SCOPUSTM
Citations
21
checked on Jan 13, 2024
Page view(s)
1,072
checked on Jan 28, 2024
Download(s)
2
checked on Jan 28, 2024
Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.