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Existence of positive solutions for one dimensional Minkowski curvature problem with singularity

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Abstract

In this paper, we consider the existence of positive solutions for one dimensional Minkowski curvature problem with either singular weight function or singular nonlinear term. By virtue of fixed point arguments and perturbation technique, we establish the new existence results of positive solutions under different assumptions on the nonlinear term. Moreover, some examples are also given as applications.

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Acknowledgements

Tingzhi Cheng is supported by the Natural Science Foundation of Shandong Province of China (ZR2021QA070). Xianghui Xu is supported by the Natural Science Foundation of Shandong Province of China (ZR2019BA032). The research is partially supported by the Shanghai Frontier Research Center of Modern Analysis. The authors would like to deeply thank all the reviewers for their insightful and constructive comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics Science, Ludong University, Yantai, 264025, Shandong, People’s Republic of China

    Tingzhi Cheng & Xianghui Xu

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  1. Tingzhi Cheng
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  2. Xianghui Xu
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Contributions

Theorem 1.1 and Theorem 1.3 were mainly completed by Xianghui Xu. Theorem 1.4 was mainly completed by Tingzhi Cheng. All authors reviewed the manuscript.

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Correspondence to Xianghui Xu.

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Cheng, T., Xu, X. Existence of positive solutions for one dimensional Minkowski curvature problem with singularity. J. Fixed Point Theory Appl. 25, 72 (2023). https://doi.org/10.1007/s11784-023-01076-6

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