Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators
In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the behavior of functions from the definition dom...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/511 |
| _version_ | 1797372689106599936 |
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| author | S.Zh. Igisinov L.D. Zhumaliyeva A.O. Suleimbekova Ye.N. Bayandiyev |
| author_facet | S.Zh. Igisinov L.D. Zhumaliyeva A.O. Suleimbekova Ye.N. Bayandiyev |
| author_sort | S.Zh. Igisinov |
| collection | DOAJ |
| description |
In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the behavior of functions from the definition domain for a differential operator with piecewise continuous coefficients in a bounded domain, which affect the spectral characteristics of boundary value problems for degenerate elliptic equations. It is shown the conditions imposed on the coefficients at the lowest terms of the equation, which ensure the existence and uniqueness of the solution. The existence, uniqueness, and smoothness of a solution are proved, and estimates are found for singular numbers (s-numbers) and eigenvalues of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration.
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| first_indexed | 2024-03-08T18:39:27Z |
| format | Article |
| id | doaj.art-edd1fc6387c44eabb233b9c5a4c83820 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:27Z |
| publishDate | 2022-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-edd1fc6387c44eabb233b9c5a4c838202023-12-29T10:19:18ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-09-01107310.31489/2022m3/51-58Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operatorsS.Zh. IgisinovL.D. ZhumaliyevaA.O. SuleimbekovaYe.N. Bayandiyev In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the behavior of functions from the definition domain for a differential operator with piecewise continuous coefficients in a bounded domain, which affect the spectral characteristics of boundary value problems for degenerate elliptic equations. It is shown the conditions imposed on the coefficients at the lowest terms of the equation, which ensure the existence and uniqueness of the solution. The existence, uniqueness, and smoothness of a solution are proved, and estimates are found for singular numbers (s-numbers) and eigenvalues of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/511elliptic operatorboundary value problemsingular numberspower degeneracysolutionuniqueness |
| spellingShingle | S.Zh. Igisinov L.D. Zhumaliyeva A.O. Suleimbekova Ye.N. Bayandiyev Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators Қарағанды университетінің хабаршысы. Математика сериясы elliptic operator boundary value problem singular numbers power degeneracy solution uniqueness |
| title | Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators |
| title_full | Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators |
| title_fullStr | Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators |
| title_full_unstemmed | Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators |
| title_short | Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators |
| title_sort | estimates of singular numbers s numbers for a class of degenerate elliptic operators |
| topic | elliptic operator boundary value problem singular numbers power degeneracy solution uniqueness |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/511 |
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