{"title":"非卷积Volterra求和方程的定性分析","authors":"Y. Raffoul","doi":"10.37622/ijde/14.1.2019.75-89","DOIUrl":null,"url":null,"abstract":"This paper is first in a series of papers in which we consider the vector nonconvolution Volterra summation equation x(t) = a(t)− t−1 ∑ s=0 C(t, s)x(s), t ∈ Z where x and a are k-vectors, k ≥ 1, while C is an k × k matrix. Fixed point theorem, combined with resolvent and Lyapunov functionals are utilized to obtain conditions for boundedness of solutions, the existence of asymptotically periodic solution and the decay of solutions to zero. AMS Subject Classifications: 34D20, 34D40, 34K20.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"22 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Qualitative Analysis of Nonconvolution Volterra Summation Equations\",\"authors\":\"Y. Raffoul\",\"doi\":\"10.37622/ijde/14.1.2019.75-89\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is first in a series of papers in which we consider the vector nonconvolution Volterra summation equation x(t) = a(t)− t−1 ∑ s=0 C(t, s)x(s), t ∈ Z where x and a are k-vectors, k ≥ 1, while C is an k × k matrix. Fixed point theorem, combined with resolvent and Lyapunov functionals are utilized to obtain conditions for boundedness of solutions, the existence of asymptotically periodic solution and the decay of solutions to zero. AMS Subject Classifications: 34D20, 34D40, 34K20.\",\"PeriodicalId\":36454,\"journal\":{\"name\":\"International Journal of Difference Equations\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Difference Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37622/ijde/14.1.2019.75-89\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Difference Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37622/ijde/14.1.2019.75-89","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Qualitative Analysis of Nonconvolution Volterra Summation Equations
This paper is first in a series of papers in which we consider the vector nonconvolution Volterra summation equation x(t) = a(t)− t−1 ∑ s=0 C(t, s)x(s), t ∈ Z where x and a are k-vectors, k ≥ 1, while C is an k × k matrix. Fixed point theorem, combined with resolvent and Lyapunov functionals are utilized to obtain conditions for boundedness of solutions, the existence of asymptotically periodic solution and the decay of solutions to zero. AMS Subject Classifications: 34D20, 34D40, 34K20.
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