{"title":"Periodic solutions for the coupled wave equations with concave-convex nonlinearities","authors":"Jianhua Liu, Jiayu Deng, Shuguan Ji","doi":"10.1016/j.jde.2025.113584","DOIUrl":null,"url":null,"abstract":"<div><div>In this work, we show that the coupled wave equations possess infinitely many time-periodic solutions. The nonlinearities are the combination of a convex term and a concave term, and we mainly focus on the effect of the concave term on the solution structure of the periodic-Dirichlet wave equations. The proof is based on the detailed analysis for the spectrum structure of the corresponding linear operator, and we obtain the existence and multiplicity of time-periodic solutions to our problem by critical point theory and approximation arguments.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113584"},"PeriodicalIF":2.4000,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625006114","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we show that the coupled wave equations possess infinitely many time-periodic solutions. The nonlinearities are the combination of a convex term and a concave term, and we mainly focus on the effect of the concave term on the solution structure of the periodic-Dirichlet wave equations. The proof is based on the detailed analysis for the spectrum structure of the corresponding linear operator, and we obtain the existence and multiplicity of time-periodic solutions to our problem by critical point theory and approximation arguments.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics