{"title":"复系数标量Riccati方程解的性质及其应用","authors":"G. Grigorian","doi":"10.7153/DEA-2018-10-20","DOIUrl":null,"url":null,"abstract":"The definition of normal and extremal solutions of the scalar Riccati equation with complex coefficients is given. Some properties of normal and extremal solutions to Riccati equation are studied. On the basis of the obtained, some theorems which describe the asymptotic behavior of solutions of the system of two linear first order ordinary differential equations are proved (in particular a minimality theorem of a solution of the system of two linear first order ordinary differential equations is proved).","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"60 1","pages":"277-298"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Properties of solutions of the scalar Riccati equation with complex coefficients and some their applications\",\"authors\":\"G. Grigorian\",\"doi\":\"10.7153/DEA-2018-10-20\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The definition of normal and extremal solutions of the scalar Riccati equation with complex coefficients is given. Some properties of normal and extremal solutions to Riccati equation are studied. On the basis of the obtained, some theorems which describe the asymptotic behavior of solutions of the system of two linear first order ordinary differential equations are proved (in particular a minimality theorem of a solution of the system of two linear first order ordinary differential equations is proved).\",\"PeriodicalId\":11162,\"journal\":{\"name\":\"Differential Equations and Applications\",\"volume\":\"60 1\",\"pages\":\"277-298\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"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-2018-10-20\",\"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-2018-10-20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Properties of solutions of the scalar Riccati equation with complex coefficients and some their applications
The definition of normal and extremal solutions of the scalar Riccati equation with complex coefficients is given. Some properties of normal and extremal solutions to Riccati equation are studied. On the basis of the obtained, some theorems which describe the asymptotic behavior of solutions of the system of two linear first order ordinary differential equations are proved (in particular a minimality theorem of a solution of the system of two linear first order ordinary differential equations is proved).
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