Periodic solutions of the $ L_p $-Minkowski problem with indefinite weight

Zhibo Cheng; Pedro J. Torres; Zhibo Cheng; Pedro J. Torres

doi:10.3934/mmc.2022002

Mathematical Modelling and Control

2022, Volume 2, Issue 1: 7-12. doi: 10.3934/mmc.2022002

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Research article

Periodic solutions of the $ L_p $-Minkowski problem with indefinite weight

Zhibo Cheng ¹,
Pedro J. Torres ^{2
,
,}

1.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China
2.
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Granada 18071, Spain

Received: 11 December 2021 Accepted: 08 January 2022 Published: 19 January 2022

We provide a new sufficient condition for the existence of a periodic solution of the singular differential equation

$ u''+u = \frac{h(t)}{u^\rho}, $

which is associated with the planar $ L_p $-Minkowski problem. A similar result is valid for the conformal version of the problem.
- $ L_p $-Minkowski problem,
- singular differential equation,
- indefinite weight,
- periodic solution
Citation: Zhibo Cheng, Pedro J. Torres. Periodic solutions of the $ L_p $-Minkowski problem with indefinite weight[J]. Mathematical Modelling and Control, 2022, 2(1): 7-12. doi: 10.3934/mmc.2022002

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Abstract

We provide a new sufficient condition for the existence of a periodic solution of the singular differential equation

$ u''+u = \frac{h(t)}{u^\rho}, $

which is associated with the planar $ L_p $-Minkowski problem. A similar result is valid for the conformal version of the problem.

References

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