{"title":"On the Solvability of Initial and Boundary Value Problems for Abstract Functional-Differential Euler–Poisson–Darboux Equations","authors":"A. V. Glushak","doi":"10.1134/s0012266124030054","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In a Banach space, we consider the Cauchy problem and the Dirichlet and Neumann\nboundary value problems for a functional-differential equation generalizing the\nEuler–Poisson–Darboux equation. A sufficient condition for the solvability of the Cauchy problem\nis proved, and an explicit form of the resolving operator is indicated, which is written using the\nBessel and Struve operator functions introduced by the author. For boundary value problems in\nthe hyperbolic case, we establish conditions imposed on the operator coefficient of the equation\nand the boundary elements that are sufficient for the unique solvability of these problems.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030054","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
In a Banach space, we consider the Cauchy problem and the Dirichlet and Neumann
boundary value problems for a functional-differential equation generalizing the
Euler–Poisson–Darboux equation. A sufficient condition for the solvability of the Cauchy problem
is proved, and an explicit form of the resolving operator is indicated, which is written using the
Bessel and Struve operator functions introduced by the author. For boundary value problems in
the hyperbolic case, we establish conditions imposed on the operator coefficient of the equation
and the boundary elements that are sufficient for the unique solvability of these problems.
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