Multiplicity of positive periodic solutions of Rayleigh equations with singularities

The existence of positive periodic solutions of the Rayleigh equations $ x''+f(x')+g(x) = e(t) $ with singularities is investigated in this paper. Based on the continuation theorem of coincidence degree theory and the method of upper and lower solutions, the multiple periodic solution...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 6; pp. 6422 - 6438
Main Authors Liang, Zaitao, Shan, Xuemeng, Wei, Hui
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
coincidence degree theory
periodic solutions
rayleigh equations
singularities
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Summary:The existence of positive periodic solutions of the Rayleigh equations $ x''+f(x')+g(x) = e(t) $ with singularities is investigated in this paper. Based on the continuation theorem of coincidence degree theory and the method of upper and lower solutions, the multiple periodic solutions of the singular Rayleigh equations can be determined under the weak conditions of the term $ g $. We discuss both the repulsive singular case and the attractive singular case. Some results in the literature are generalized and improved. Moreover, some examples and numerical simulations are given to illustrate our theoretical analysis.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021377