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2018 Global structure of positive solutions for problem with mean curvature operator on an annular domain
Xiaofei Cao, Guowei Dai, Ning Zhang
Rocky Mountain J. Math. 48(6): 1799-1814 (2018). DOI: 10.1216/RMJ-2018-48-6-1799

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.

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Xiaofei Cao. Guowei Dai. Ning Zhang. "Global structure of positive solutions for problem with mean curvature operator on an annular domain." Rocky Mountain J. Math. 48 (6) 1799 - 1814, 2018. https://doi.org/10.1216/RMJ-2018-48-6-1799

Information

Published: 2018
First available in Project Euclid: 24 November 2018

zbMATH: 06987225
MathSciNet: MR3879302
Digital Object Identifier: 10.1216/RMJ-2018-48-6-1799

Subjects:
Primary: 35B32, 35B40, 53A10

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 6 • 2018
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