{"title":"基于Euler-Bernoulli方程的悬臂梁四阶微分包含的正解","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":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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}
Positive solutions for a fourth order differential inclusion based on the Euler-Bernoulli equation for a Cantilever beam
. 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.