{"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":50580,"journal":{"name":"Differential Equations","volume":"20 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030054","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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