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Research Article | Open Access

Bifurcation curves of positive solutions for one-dimensional Minkowski curvature problem

Zhiqian He1( ), Man Xu2, Yanzhong Zhao1, Xiaobin Yao3
School of Mathematics and Physics, Qinghai University, Xining 810016, China
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
School of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China
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Abstract

In this paper, we study the shape of the bifurcation curves of positive solutions for the one-dimensional Minkowski-curvature problem. By developing some new time mapping techniques, we find that the bifurcation curve is ⊂-shaped/monotone increasing/ S-like shaped on the ( λ , | | u | | ∞ ) plane when the nonlinearity satisfies different assumptions. Finally, two examples are given to illustrate our result.

Keywords

mean curvature equationpositive solutionsbifurcation curvetime mappingexistence
CLC number: 34C23, 35J60, 34B18

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 17001-17018
DOI: 10.3934/math.2022934

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Cite this article:
He Z, Xu M, Zhao Y, et al. Bifurcation curves of positive solutions for one-dimensional Minkowski curvature problem. AIMS Mathematics, 2022, 7(9): 17001-17018. https://doi.org/10.3934/math.2022934

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Received: 19 May 2022
Revised: 29 June 2022
Accepted: 04 July 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)