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Pseudosolution of an integral convolution equation of the first kind.

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Title: Pseudosolution of an integral convolution equation of the first kind.
Authors: Yengibaryan, N. B.1 (AUTHOR) yengib@instmath.sci.am
Source: Theoretical & Mathematical Physics. May2025, Vol. 223 Issue 2, p872-877. 6p.
Subjects: Absolute continuity, Integral equations, Equations
Abstract: We consider the equation , where and the functions and and their first derivatives are absolutely continuous on and . An arbitrary term is added to the right-hand side of the equation. The obtained family of equations is reduced by double differentiation to an equation of the second kind. In the case of its unique solvability in , the solution is called a -pseudosolution of the original equation. We introduce the partial regularization of the equation and present some cases of the existence of a -pseudosolution. We propose a criterion for the suitability of as an approximate solution. The problem of constructing a pseudosolution of an equation on the half-line is discussed. [ABSTRACT FROM AUTHOR]
Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Pseudosolution of an integral convolution equation of the first kind.
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  Data: We consider the equation , where and the functions and and their first derivatives are absolutely continuous on and . An arbitrary term is added to the right-hand side of the equation. The obtained family of equations is reduced by double differentiation to an equation of the second kind. In the case of its unique solvability in , the solution is called a -pseudosolution of the original equation. We introduce the partial regularization of the equation and present some cases of the existence of a -pseudosolution. We propose a criterion for the suitability of as an approximate solution. The problem of constructing a pseudosolution of an equation on the half-line is discussed. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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