Rocky Mountain Journal of Mathematics

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

Xiaofei Cao, Guowei Dai, and Ning Zhang

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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


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