{"title":"具有双重特征值的非线性二阶q差分方程的解析通解","authors":"Mami Suzuki","doi":"10.4171/rsmup/89","DOIUrl":null,"url":null,"abstract":"As far as the author knows it seems that an existence theorem of a solution of a general nonlinear q-difference equation is not known. In this paper we will investigate a nonlinear second order q-difference equation whose characteristic equation has only one solution and will show analytic general solutions of such an equation. Further we will show an example. Mathematics Subject Classification (2010). Primary: 39A13; Secondary: 39A45.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytic general solutions of nonlinear second-order $q$-difference equations with a double characteristic value\",\"authors\":\"Mami Suzuki\",\"doi\":\"10.4171/rsmup/89\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"As far as the author knows it seems that an existence theorem of a solution of a general nonlinear q-difference equation is not known. In this paper we will investigate a nonlinear second order q-difference equation whose characteristic equation has only one solution and will show analytic general solutions of such an equation. Further we will show an example. Mathematics Subject Classification (2010). Primary: 39A13; Secondary: 39A45.\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"44 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/rsmup/89\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/89","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Analytic general solutions of nonlinear second-order $q$-difference equations with a double characteristic value
As far as the author knows it seems that an existence theorem of a solution of a general nonlinear q-difference equation is not known. In this paper we will investigate a nonlinear second order q-difference equation whose characteristic equation has only one solution and will show analytic general solutions of such an equation. Further we will show an example. Mathematics Subject Classification (2010). Primary: 39A13; Secondary: 39A45.
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