{"title":"Infinitely many fast homoclinic solutions for different classes of damped vibration systems","authors":"M. Timoumi","doi":"10.23952/jnfa.2020.46","DOIUrl":null,"url":null,"abstract":". In this paper, we study the existence and multiplicity of fast homoclinic orbits for the class of damped vibration systems ¨ where L ( t ) is not required to be either uniformly positive definite or coercive, and W ( t , x ) is of subquadratic or superquadratic growth as | x | → ∞ , or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic at infinity). To the best of our knowl-edge, there is no result concerning the existence and multiplicity of homoclinic orbits for the system with the conditions.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/jnfa.2020.46","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
. In this paper, we study the existence and multiplicity of fast homoclinic orbits for the class of damped vibration systems ¨ where L ( t ) is not required to be either uniformly positive definite or coercive, and W ( t , x ) is of subquadratic or superquadratic growth as | x | → ∞ , or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic at infinity). To the best of our knowl-edge, there is no result concerning the existence and multiplicity of homoclinic orbits for the system with the conditions.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.