{"title":"哈默斯坦式弱奇异积分方程的边值问题","authors":"Oleksandr Boichuk, Viktor Feruk","doi":"10.1007/s11253-024-02307-w","DOIUrl":null,"url":null,"abstract":"<p>We consider the problem of existence of the solution of a weakly nonlinear boundary-value problem for the Hammerstein-type integral equation with unbounded kernel, which turns, for <i>ε</i> = 0, into one of solutions of the generating problem. The necessary and sufficient conditions for the existence of this solution are obtained and the iterative procedure is proposed for its construction.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"51 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boundary-Value Problems for Weakly Singular Integral Equations of Hammerstein Type\",\"authors\":\"Oleksandr Boichuk, Viktor Feruk\",\"doi\":\"10.1007/s11253-024-02307-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider the problem of existence of the solution of a weakly nonlinear boundary-value problem for the Hammerstein-type integral equation with unbounded kernel, which turns, for <i>ε</i> = 0, into one of solutions of the generating problem. The necessary and sufficient conditions for the existence of this solution are obtained and the iterative procedure is proposed for its construction.</p>\",\"PeriodicalId\":49406,\"journal\":{\"name\":\"Ukrainian Mathematical Journal\",\"volume\":\"51 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ukrainian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11253-024-02307-w\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ukrainian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02307-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Boundary-Value Problems for Weakly Singular Integral Equations of Hammerstein Type
We consider the problem of existence of the solution of a weakly nonlinear boundary-value problem for the Hammerstein-type integral equation with unbounded kernel, which turns, for ε = 0, into one of solutions of the generating problem. The necessary and sufficient conditions for the existence of this solution are obtained and the iterative procedure is proposed for its construction.
期刊介绍：
Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries.
Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.
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