Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line
We consider a class of nonlinear integral equations with a stochastic and symmetric kernel on the whole line. With certain particular representations of the kernel and nonlinearity, equations of the mentioned type arise in many branches of mathematical natural science. In particular, such equations...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2022-09-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/106733/pdf |
| _version_ | 1811167069743349760 |
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| author | Khachatur A. Khachatryan Haykanush S. Petrosyan |
| author_facet | Khachatur A. Khachatryan Haykanush S. Petrosyan |
| author_sort | Khachatur A. Khachatryan |
| collection | DOAJ |
| description | We consider a class of nonlinear integral equations with a stochastic and symmetric kernel on the whole line. With certain particular representations of the kernel and nonlinearity, equations of the mentioned type arise in many branches of mathematical natural science. In particular, such equations occur in the theoryp-adic strings, in the kinetic theory of gases, in mathematical biology and in the theory of radiative transfer. Constructive existence theorems are proved for non-negative non-trivial and bounded solutions under various restrictions on the function describing the nonlinearity in the equation. Under additional restrictions on the kernel and on the nonlinearity, a uniqueness theorem is also proved in a certain class of bounded and non-negative functions that have a finite limit in.At the end, specific applied examples of the kernel and non-linearity are given that satisfy to all restrictions of the proven statements. |
| first_indexed | 2024-04-10T16:04:06Z |
| format | Article |
| id | doaj.art-cdeb49eb21074e19944599e6b6c69403 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-10T16:04:06Z |
| publishDate | 2022-09-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-cdeb49eb21074e19944599e6b6c694032023-02-10T08:13:31ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812022-09-0126344647910.14498/vsgtu193277828Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole lineKhachatur A. Khachatryan0https://orcid.org/0000-0002-4835-943XHaykanush S. Petrosyan1https://orcid.org/0000-0002-7172-4730Yerevan State UniversityArmenian National Agrarian UniversityWe consider a class of nonlinear integral equations with a stochastic and symmetric kernel on the whole line. With certain particular representations of the kernel and nonlinearity, equations of the mentioned type arise in many branches of mathematical natural science. In particular, such equations occur in the theoryp-adic strings, in the kinetic theory of gases, in mathematical biology and in the theory of radiative transfer. Constructive existence theorems are proved for non-negative non-trivial and bounded solutions under various restrictions on the function describing the nonlinearity in the equation. Under additional restrictions on the kernel and on the nonlinearity, a uniqueness theorem is also proved in a certain class of bounded and non-negative functions that have a finite limit in.At the end, specific applied examples of the kernel and non-linearity are given that satisfy to all restrictions of the proven statements.https://journals.eco-vector.com/1991-8615/article/viewFile/106733/pdfmonotonicitysuccessive approximationsconvergencebounded solutionsolution limitcaratheodory condition |
| spellingShingle | Khachatur A. Khachatryan Haykanush S. Petrosyan Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki monotonicity successive approximations convergence bounded solution solution limit caratheodory condition |
| title | Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line |
| title_full | Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line |
| title_fullStr | Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line |
| title_full_unstemmed | Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line |
| title_short | Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line |
| title_sort | questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line |
| topic | monotonicity successive approximations convergence bounded solution solution limit caratheodory condition |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/106733/pdf |
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