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Existence results for Dirichlet problems about two mean curvature equations in Euclidean and Minkowski spaces

  • Yaning WangEmail author
Article
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Abstract

Let \(H_L\) and \(H_R\) be the extrinsic mean curvatures of a spacelike graph in Minkowski space \(\mathbb {L}^{N+1}\) and Euclidean space \(\mathbb {R}^{N+1}\), respectively. In this paper, we establish the existence of multiple positive radial solutions for the Dirichlet problem of two nonlinear partial differential equations involving \(H_L\) and \(H_R\).

Keywords

Dirichlet problem multiple radial solution mean curvature equation fixed-point theorem of cone expansion/compression type 

Mathematics Subject Classification

35J93 35J25 35A01 53C42 

Notes

Acknowledgements

I would like to thank the anonymous reviewer for his or her valuable suggestions that improves the original manuscript. The author was supported by the Youth Science Foundation of Henan Normal University (no. 2014QK01).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information SciencesHenan Normal UniversityXinxiangPeople’s Republic of China

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