Positive radial solutions of a mean curvature equation in Minkowski space with strong singularity
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- by Minghe Pei and Libo Wang PDF
- Proc. Amer. Math. Soc. 145 (2017), 4423-4430 Request permission
Abstract:
The existence of positive radial solution is obtained for a mean curvature equation in Minkowski space of the form \[ \left \{ \begin {array}{ll} \hbox {div}(\frac {\nabla v}{\sqrt {1-|\nabla v|^2}})+f(|x|,v)=0\quad \textrm {in}\quad \Omega ; \\ v=0\quad \textrm {on}\quad \partial \Omega , \end {array} \right . \] where $\Omega$ is a unit ball in $\mathbb {R}^N$, $f(r,u)$ has singularities at $u=0$, $r=0$ and/or $r=1$. The main tool is the perturbation technique and nonlinear alternative of Leray-Schauder type. The interesting point is that the nonlinear term $f(r,u)$ at $u=0$ may be strongly singular.References
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Additional Information
- Minghe Pei
- Affiliation: School of Mathematics and Statistics, Beihua University, JiLin City 132013, People’s Republic of China
- MR Author ID: 600637
- Email: peiminghe@163.com
- Libo Wang
- Affiliation: School of Mathematics and Statistics, Beihua University, JiLin City 132013, People’s Republic of China
- Email: wlb$_$math@163.com
- Received by editor(s): July 31, 2016
- Received by editor(s) in revised form: November 12, 2016
- Published electronically: April 28, 2017
- Additional Notes: This project was sponsored by the Education Department of JiLin Province of China ([2016]45)
- Communicated by: Joachim Krieger
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4423-4430
- MSC (2010): Primary 35J93, 35J75, 35A20
- DOI: https://doi.org/10.1090/proc/13587
- MathSciNet review: 3690625