{"title":"Caratheodory periodic perturbations of degenerate systems","authors":"A. Calamai, M. Spadini","doi":"10.58997/ejde.2024.39","DOIUrl":null,"url":null,"abstract":"We study the structure of the set of harmonic solutions to T-periodically perturbed coupled differential equations on differentiable manifolds, where the perturbation is allowed to be of Caratheodory-type regularity. Employing degree-theoretic methods, we prove the existence of a noncompact connected set of nontrivial T-periodic solutions that, in a sense, emanates from the set of zeros of the unperturbed vector field. The latter is assumed to be ''degenerate'': Meaning that, contrary to the usual assumptions on the leading vector field, it is not required to be either trivial nor to have a compact set of zeros. In fact, known results in the ``nondegenerate case can be recovered from our ones. We also provide some illustrating examples of Lienard- and \\(\\phi\\)-Laplacian-type perturbed equations.\nFor more information see https://ejde.math.txstate.edu/Volumes/2024/39/abstr.html","PeriodicalId":0,"journal":{"name":"","volume":"101 45","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.58997/ejde.2024.39","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the structure of the set of harmonic solutions to T-periodically perturbed coupled differential equations on differentiable manifolds, where the perturbation is allowed to be of Caratheodory-type regularity. Employing degree-theoretic methods, we prove the existence of a noncompact connected set of nontrivial T-periodic solutions that, in a sense, emanates from the set of zeros of the unperturbed vector field. The latter is assumed to be ''degenerate'': Meaning that, contrary to the usual assumptions on the leading vector field, it is not required to be either trivial nor to have a compact set of zeros. In fact, known results in the ``nondegenerate case can be recovered from our ones. We also provide some illustrating examples of Lienard- and \(\phi\)-Laplacian-type perturbed equations.
For more information see https://ejde.math.txstate.edu/Volumes/2024/39/abstr.html