## Rocky Mountain Journal of Mathematics

- Rocky Mountain J. Math.
- Volume 48, Number 6 (2018), 1799-1814.

### Global structure of positive solutions for problem with mean curvature operator on an annular domain

Xiaofei Cao, Guowei Dai, and Ning Zhang

#### Abstract

We study the global structure of positive solutions of the following mean curvature equation in the Minkowski space \[ -\div \bigg (\frac {\nabla u}{\sqrt {1-\vert \nabla u\vert ^2}}\bigg )= \lambda f(x,u), \] on an annular domain with the Robin boundary condition. According to the behavior of $f$ near $0$, we obtain the existence and multiplicity of positive solutions for this problem.

#### Article information

**Source**

Rocky Mountain J. Math., Volume 48, Number 6 (2018), 1799-1814.

**Dates**

First available in Project Euclid: 24 November 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.rmjm/1543028438

**Digital Object Identifier**

doi:10.1216/RMJ-2018-48-6-1799

**Mathematical Reviews number (MathSciNet)**

MR3879302

**Zentralblatt MATH identifier**

06987225

**Subjects**

Primary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35B40: Asymptotic behavior of solutions 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

**Keywords**

Bifurcation mean curvature operator positive solution

#### Citation

Cao, Xiaofei; Dai, Guowei; Zhang, Ning. Global structure of positive solutions for problem with mean curvature operator on an annular domain. Rocky Mountain J. Math. 48 (2018), no. 6, 1799--1814. doi:10.1216/RMJ-2018-48-6-1799. https://projecteuclid.org/euclid.rmjm/1543028438