{"title":"三阶边值问题解的存在唯一性:闭集和有界集的分析","authors":"S. S. Almuthaybiri, C. Tisdell","doi":"10.7153/dea-2020-12-19","DOIUrl":null,"url":null,"abstract":"The aim of this work is to develop a fuller theory regarding the existence, uniqueness and approximation of solutions to third-order boundary value problems via fixed point methods. To develop this deeper understanding of qualitative properties of solutions, our strategy involves an analysis of the problem under consideration, and its associated operator equations, within closed and bounded sets. This enables our new results to apply to a wider range of problems than those covered in the recent literature and we discuss several examples to illustrate the nature of these advancements. Mathematics subject classification (2010): 34B15.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Existence and uniqueness of solutions to third-order boundary value problems: analysis in closed and bounded sets\",\"authors\":\"S. S. Almuthaybiri, C. Tisdell\",\"doi\":\"10.7153/dea-2020-12-19\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this work is to develop a fuller theory regarding the existence, uniqueness and approximation of solutions to third-order boundary value problems via fixed point methods. To develop this deeper understanding of qualitative properties of solutions, our strategy involves an analysis of the problem under consideration, and its associated operator equations, within closed and bounded sets. This enables our new results to apply to a wider range of problems than those covered in the recent literature and we discuss several examples to illustrate the nature of these advancements. Mathematics subject classification (2010): 34B15.\",\"PeriodicalId\":11162,\"journal\":{\"name\":\"Differential Equations and Applications\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/dea-2020-12-19\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/dea-2020-12-19","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Existence and uniqueness of solutions to third-order boundary value problems: analysis in closed and bounded sets
The aim of this work is to develop a fuller theory regarding the existence, uniqueness and approximation of solutions to third-order boundary value problems via fixed point methods. To develop this deeper understanding of qualitative properties of solutions, our strategy involves an analysis of the problem under consideration, and its associated operator equations, within closed and bounded sets. This enables our new results to apply to a wider range of problems than those covered in the recent literature and we discuss several examples to illustrate the nature of these advancements. Mathematics subject classification (2010): 34B15.
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