On Integral Equations the Kernels of Which are Homogeneous Functions of Degree (−1)
The present paper deals with integral equations the kernels of which are homogeneous functions of degree (−1). Factorization approach to such equations is developed. The constructed operator factorization is applied to the equation with a positive symmetric kernel. We prove that in the conservative...
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| Vydáno v: | Journal of contemporary mathematical analysis Ročník 53; číslo 1; s. 47 - 55 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Moscow
Pleiades Publishing
01.01.2018
Springer Nature B.V |
| Témata: | |
| ISSN: | 1068-3623, 1934-9416 |
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| Abstract | The present paper deals with integral equations the kernels of which are homogeneous functions of degree (−1). Factorization approach to such equations is developed. The constructed operator factorization is applied to the equation with a positive symmetric kernel. We prove that in the conservative case, both the homogeneous equation and the corresponding nonhomogeneous equation with a positive free term can possess positive solutions simultaneously. |
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| AbstractList | The present paper deals with integral equations the kernels of which are homogeneous functions of degree (−1). Factorization approach to such equations is developed. The constructed operator factorization is applied to the equation with a positive symmetric kernel. We prove that in the conservative case, both the homogeneous equation and the corresponding nonhomogeneous equation with a positive free term can possess positive solutions simultaneously. |
| Author | Barseghyan, A. G. |
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| Cites_doi | 10.1007/BF01085507 10.4213/sm529 |
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| Copyright | Allerton Press, Inc. 2018 Copyright Springer Science & Business Media 2018 |
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| Keywords | conservative equation homogeneous function of degree −1 Nonlinear factorization equation fundamental solution |
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| References | Arabadzhyan, Engibarian (CR6) 1987; 36 Titchmarsh (CR2) 1948 Dixon (CR1) 1926; 27 Krein (CR3) 1958; 13 Sakhnovich (CR4) 2007 Engibaryan (CR7) 2000; 191 Engibaryan, Arutyunyan (CR5) 1975; 97 A. C. Dixon (6327_CR1) 1926; 27 L. A. Sakhnovich (6327_CR4) 2007 N. B. Engibaryan (6327_CR7) 2000; 191 E. Titchmarsh (6327_CR2) 1948 N. B. Engibaryan (6327_CR5) 1975; 97 M. G. Krein (6327_CR3) 1958; 13 L.G. Arabadzhyan (6327_CR6) 1987; 36 |
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| StartPage | 47 |
| SubjectTerms | Factorization Integral Equations Kernels Mathematical analysis Mathematics Mathematics and Statistics Operators (mathematics) |
| Title | On Integral Equations the Kernels of Which are Homogeneous Functions of Degree (−1) |
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