{"title":"具有变符号强迫项的非自治Duffing方程的参数相关周期问题","authors":"Jiri Sremr","doi":"10.58997/ejde.2023.65","DOIUrl":null,"url":null,"abstract":"We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem $$ u''=p(t)u+h(t)|u|^{\\lambda}\\operatorname{sgn} u+\\mu f(t);\\quad u(0)=u(\\omega),\\; u'(0)=u'(\\omega), $$ where \\(\\mu\\in \\mathbb{R}\\) is a parameter. We assume that \\(p,h,f\\in L([0,\\omega])\\), \\(\\lambda>1\\), and the function \\(h\\) is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term \\(f\\) to change its sign.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/65/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"301 1","pages":"0"},"PeriodicalIF":0.8000,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term\",\"authors\":\"Jiri Sremr\",\"doi\":\"10.58997/ejde.2023.65\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem $$ u''=p(t)u+h(t)|u|^{\\\\lambda}\\\\operatorname{sgn} u+\\\\mu f(t);\\\\quad u(0)=u(\\\\omega),\\\\; u'(0)=u'(\\\\omega), $$ where \\\\(\\\\mu\\\\in \\\\mathbb{R}\\\\) is a parameter. We assume that \\\\(p,h,f\\\\in L([0,\\\\omega])\\\\), \\\\(\\\\lambda>1\\\\), and the function \\\\(h\\\\) is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term \\\\(f\\\\) to change its sign.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/65/abstr.html\",\"PeriodicalId\":49213,\"journal\":{\"name\":\"Electronic Journal of Differential Equations\",\"volume\":\"301 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.58997/ejde.2023.65\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.58997/ejde.2023.65","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term
We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem $$ u''=p(t)u+h(t)|u|^{\lambda}\operatorname{sgn} u+\mu f(t);\quad u(0)=u(\omega),\; u'(0)=u'(\omega), $$ where \(\mu\in \mathbb{R}\) is a parameter. We assume that \(p,h,f\in L([0,\omega])\), \(\lambda>1\), and the function \(h\) is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term \(f\) to change its sign.
For more information see https://ejde.math.txstate.edu/Volumes/2023/65/abstr.html
期刊介绍:
All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.