{"title":"非线性四阶两点边值问题的存在性","authors":"R. Agarwal, Gabriela Mihaylova, P. Kelevedjiev","doi":"10.3390/dynamics3010010","DOIUrl":null,"url":null,"abstract":"The present paper is devoted to the solvability of various two-point boundary value problems for the equation y(4)=f(t,y,y′,y″,y‴), where the nonlinearity f may be defined on a bounded set and is needed to be continuous on a suitable subset of its domain. The established existence results guarantee not just a solution to the considered boundary value problems but also guarantee the existence of monotone solutions with suitable signs and curvature. The obtained results rely on a basic existence theorem, which is a variant of a theorem due to A. Granas, R. Guenther and J. Lee. The a priori bounds necessary for the application of the basic theorem are provided by the barrier strip technique. The existence results are illustrated with examples.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Existence for Nonlinear Fourth-Order Two-Point Boundary Value Problems\",\"authors\":\"R. Agarwal, Gabriela Mihaylova, P. Kelevedjiev\",\"doi\":\"10.3390/dynamics3010010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The present paper is devoted to the solvability of various two-point boundary value problems for the equation y(4)=f(t,y,y′,y″,y‴), where the nonlinearity f may be defined on a bounded set and is needed to be continuous on a suitable subset of its domain. The established existence results guarantee not just a solution to the considered boundary value problems but also guarantee the existence of monotone solutions with suitable signs and curvature. The obtained results rely on a basic existence theorem, which is a variant of a theorem due to A. Granas, R. Guenther and J. Lee. The a priori bounds necessary for the application of the basic theorem are provided by the barrier strip technique. The existence results are illustrated with examples.\",\"PeriodicalId\":80276,\"journal\":{\"name\":\"Dynamics (Pembroke, Ont.)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dynamics (Pembroke, Ont.)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/dynamics3010010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamics (Pembroke, Ont.)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/dynamics3010010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
本文研究方程y(4)=f(t,y,y ',y″,y )的各种两点边值问题的可解性,其中非线性f可以定义在有界集合上,并且需要在其定义域的适当子集上连续。所建立的存在性结果不仅保证了所考虑的边值问题的解,而且保证了具有合适符号和曲率的单调解的存在性。得到的结果依赖于一个基本存在定理,它是a . Granas, R. Guenther和J. Lee的定理的变体。障条技术提供了应用基本定理所必需的先验界。用实例说明了存在性结果。
Existence for Nonlinear Fourth-Order Two-Point Boundary Value Problems
The present paper is devoted to the solvability of various two-point boundary value problems for the equation y(4)=f(t,y,y′,y″,y‴), where the nonlinearity f may be defined on a bounded set and is needed to be continuous on a suitable subset of its domain. The established existence results guarantee not just a solution to the considered boundary value problems but also guarantee the existence of monotone solutions with suitable signs and curvature. The obtained results rely on a basic existence theorem, which is a variant of a theorem due to A. Granas, R. Guenther and J. Lee. The a priori bounds necessary for the application of the basic theorem are provided by the barrier strip technique. The existence results are illustrated with examples.