Existence and bifurcation of periodic solutions to the Lp-Minkowski problem with indefinite weight

被引：1

作者：

Cheng, Zhibo ^{[1
]}

Xia, Chenyang ^{[1
]}

Yuan, Qigang ^{[2
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Peoples R China

[2] North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450046, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 534卷 / 01期

关键词：

Lp-Minkowski problem; Periodic solution; Existence; Bifurcation; Indefinite singularity; DIFFERENTIAL-EQUATIONS;

D O I：

10.1016/j.jmaa.2023.128074

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the existence and bifurcation of positive periodic solutions for Lp-Minkowski problem with indefinite weight. We provide new sufficient conditions for the existence of at least one positive periodic solution. The main tools are Leray-Schauder alternative principle and a global continuation theorem by Manasevich-Mawhin. Using the numerical bifurcation theory, we study the dynamic behaviors of periodic solutions in the cases of indefinite and positive weight, where the weight term is a simple sinusoidal function. In the positive weight case, the multiplicity of positive periodic solutions is detected for the first time in the LpMinkowski problem, which is generated by a saddle-node bifurcation. (c) 2024 Elsevier Inc. All rights reserved.

引用

页数：20

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