{"title":"二阶非线性差分方程的单调解","authors":"Lianwen Wang, Anthony Willett","doi":"10.30495/JME.V0I0.2101","DOIUrl":null,"url":null,"abstract":"Classification, boundedness, and existence of solutions of a second order nonlinear difference equation are investigated. First, it is proved that all solutions are eventually monotone. Then, the necessary and sufficient conditions for the boundedness of all solutions are established. Finally, the existence of different types of monotonic solutions are presented. The obtained results have extended and improved some existing ones.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Monotonic Solutions of Second Order Nonlinear Difference Equations\",\"authors\":\"Lianwen Wang, Anthony Willett\",\"doi\":\"10.30495/JME.V0I0.2101\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Classification, boundedness, and existence of solutions of a second order nonlinear difference equation are investigated. First, it is proved that all solutions are eventually monotone. Then, the necessary and sufficient conditions for the boundedness of all solutions are established. Finally, the existence of different types of monotonic solutions are presented. The obtained results have extended and improved some existing ones.\",\"PeriodicalId\":43745,\"journal\":{\"name\":\"Journal of Mathematical Extension\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Extension\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30495/JME.V0I0.2101\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Extension","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30495/JME.V0I0.2101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Monotonic Solutions of Second Order Nonlinear Difference Equations
Classification, boundedness, and existence of solutions of a second order nonlinear difference equation are investigated. First, it is proved that all solutions are eventually monotone. Then, the necessary and sufficient conditions for the boundedness of all solutions are established. Finally, the existence of different types of monotonic solutions are presented. The obtained results have extended and improved some existing ones.
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