{"title":"一类非线性二维卷积型积分方程的交替有界解","authors":"K. Khachatryan, A. Petrosyan","doi":"10.1090/mosc/329","DOIUrl":null,"url":null,"abstract":"This paper is devoted to studying a class of nonlinear two-dimensional convolution-type integral equations on \n\n \n \n \n R\n \n 2\n \n \\mathbb {R}^2\n \n\n. This class of equations has applications in the theory of \n\n \n p\n p\n \n\n-adic open-closed strings and in the mathematical theory of the spread of epidemics in space and time. The existence of an alternating bounded solution is proved. The asymptotic behaviour of the constructed solution is also studied in a particular case. At the end of the paper, specific applied examples of these equations are given to illustrate the results. UDK 517.968.4.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Alternating bounded solutions of a class of nonlinear two-dimensional convolution-type integral equations\",\"authors\":\"K. Khachatryan, A. Petrosyan\",\"doi\":\"10.1090/mosc/329\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is devoted to studying a class of nonlinear two-dimensional convolution-type integral equations on \\n\\n \\n \\n \\n R\\n \\n 2\\n \\n \\\\mathbb {R}^2\\n \\n\\n. This class of equations has applications in the theory of \\n\\n \\n p\\n p\\n \\n\\n-adic open-closed strings and in the mathematical theory of the spread of epidemics in space and time. The existence of an alternating bounded solution is proved. The asymptotic behaviour of the constructed solution is also studied in a particular case. At the end of the paper, specific applied examples of these equations are given to illustrate the results. UDK 517.968.4.\",\"PeriodicalId\":37924,\"journal\":{\"name\":\"Transactions of the Moscow Mathematical Society\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the Moscow Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/mosc/329\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Moscow Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mosc/329","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
Alternating bounded solutions of a class of nonlinear two-dimensional convolution-type integral equations
This paper is devoted to studying a class of nonlinear two-dimensional convolution-type integral equations on
R
2
\mathbb {R}^2
. This class of equations has applications in the theory of
p
p
-adic open-closed strings and in the mathematical theory of the spread of epidemics in space and time. The existence of an alternating bounded solution is proved. The asymptotic behaviour of the constructed solution is also studied in a particular case. At the end of the paper, specific applied examples of these equations are given to illustrate the results. UDK 517.968.4.
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