Positive radial solutions of a mean curvature equation in Lorentz–Minkowski space with strong singularity. Issue 9 (3rd July 2020)

• Record Type: Journal Article
• Authors: Pei, Minghe; Wang, Libo
• Is Part Of: Applicable analysis. Volume 99:Issue 9(2020)
• Page Start: 1631
• Page End: 1637
• Publication Date: 2020-07-03
• Subjects: Mean curvature equation -- strong singularity -- radial solution -- Schauder fixed point theorem -- existence and uniqueness; 35J93 -- 35J75 -- 35A20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1555322
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: The existence and uniqueness of positive radial solutions are obtained for a mean curvature equation in Lorentz–Minkowski space of the form div ∇ v 1 − | ∇ v | 2 + f ( | x |, v ) = 0 in Ω, v = 0 on ∂Ω, where Ω is a unit ball in R N, f ( r, u ) may be singular at r =0 and/or r =1, and strongly singular at u =0. The main tool is the perturbation technique and Schauder fixed point theorem.