{"title":"论二次乌里索恩积分方程无限系统的无穷大处消失解","authors":"Józef Banaś, Justyna Madej","doi":"10.12775/tmna.2023.046","DOIUrl":null,"url":null,"abstract":"The paper is devoted to present a result on the existence of solutions of an infinite system of quadratic integral equations of \nthe Urysohn type considered on the real half-axis. Our investigations are conducted in the Banach space consisting of bounded and continuous functions\ndefined on the real half-axis with values in the space of real sequences converging to zero. That space is equipped with the standard supremum norm. \nThe main tools used in our study is the technique of measures of noncompactness and the Schauder fixed point principle. \nWe illustrate our result by a suitable example.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On solutions vanishing at infinity of infinite systems of quadratic Urysohn integral equations\",\"authors\":\"Józef Banaś, Justyna Madej\",\"doi\":\"10.12775/tmna.2023.046\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper is devoted to present a result on the existence of solutions of an infinite system of quadratic integral equations of \\nthe Urysohn type considered on the real half-axis. Our investigations are conducted in the Banach space consisting of bounded and continuous functions\\ndefined on the real half-axis with values in the space of real sequences converging to zero. That space is equipped with the standard supremum norm. \\nThe main tools used in our study is the technique of measures of noncompactness and the Schauder fixed point principle. \\nWe illustrate our result by a suitable example.\",\"PeriodicalId\":23130,\"journal\":{\"name\":\"Topological Methods in Nonlinear Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-03-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topological Methods in Nonlinear Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.12775/tmna.2023.046\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topological Methods in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12775/tmna.2023.046","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On solutions vanishing at infinity of infinite systems of quadratic Urysohn integral equations
The paper is devoted to present a result on the existence of solutions of an infinite system of quadratic integral equations of
the Urysohn type considered on the real half-axis. Our investigations are conducted in the Banach space consisting of bounded and continuous functions
defined on the real half-axis with values in the space of real sequences converging to zero. That space is equipped with the standard supremum norm.
The main tools used in our study is the technique of measures of noncompactness and the Schauder fixed point principle.
We illustrate our result by a suitable example.
期刊介绍:
Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.