{"title":"Positive solutions for a fourth order differential inclusion based on the Euler-Bernoulli equation for a Cantilever beam","authors":"John S. Spraker","doi":"10.7153/dea-2019-11-26","DOIUrl":null,"url":null,"abstract":". An existence result for positive solutions to a fourth order differential inclusion with boundary values is given. This is accomplished by using a fi xed point theorem on cones for multivalued maps, L 1 selections and a generalization of the Ascoli theorem. The inclusion allows the function and its fi rst three derivatives to be on the right-hand side. The proof involves a Green’s function and a positive eigenvalue of a particular operator. An example is provided.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/dea-2019-11-26","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
. An existence result for positive solutions to a fourth order differential inclusion with boundary values is given. This is accomplished by using a fi xed point theorem on cones for multivalued maps, L 1 selections and a generalization of the Ascoli theorem. The inclusion allows the function and its fi rst three derivatives to be on the right-hand side. The proof involves a Green’s function and a positive eigenvalue of a particular operator. An example is provided.