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New Existence Results of the Planar \(L_p\) Dual Minkowski Problem

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Abstract

We provide new sufficient conditions for the existence of a periodic solution of the second-order differential equation

$$\begin{aligned} u''+u=u^{p-1}(u^2+u'^2)^{\frac{2-q}{2}}f(t), \end{aligned}$$

which is associated to the planar \(L_p\) dual Minkowski problem in convex geometry. The obtained conditions are complementary to recent results. The main tools in the proofs are a global continuation theorem by Manasevich-Mawhin and a fixed point theorem of compact operators defined in conical shells of a Banach space.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454003, China

    Zhibo Cheng

  2. Departamento de Matemática Aplicada and Research Unit “Modeling Nature” (MNat), Facultad de Ciencias, Universidad de Granada, Granada, 18071, Spain

    Pedro J. Torres

Authors
  1. Zhibo Cheng
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  2. Pedro J. Torres
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Correspondence to Pedro J. Torres.

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The fisrt author is supported by National Natural Science Foundation of China (11501170), Technological Innovation Talents in Universities and Colleges in Henan Province (21HASTIT025), Natural Science Foundation of Henan Province (222300420449) and Innovative Research Team of Henan Polytechnic University (T2022-7). The second author is partially supproted by the national research project MCIU-22-PID2021-128418NA-I00.

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Cheng, Z., Torres, P.J. New Existence Results of the Planar \(L_p\) Dual Minkowski Problem. J Geom Anal 34, 40 (2024). https://doi.org/10.1007/s12220-023-01493-6

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  • DOI: https://doi.org/10.1007/s12220-023-01493-6

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