{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02307-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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