Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary Conditions
The article considers third-order equations with multiple characteristics with general boundary value conditions and non-local initial data. A regular solution to the problem with known methods is constructed here. The uniqueness of the solution to the problem is proved by the method of energy integ...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/2/110 |
| _version_ | 1797531669576548352 |
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| author | Abdukomil Risbekovich Khashimov Dana Smetanová |
| author_facet | Abdukomil Risbekovich Khashimov Dana Smetanová |
| author_sort | Abdukomil Risbekovich Khashimov |
| collection | DOAJ |
| description | The article considers third-order equations with multiple characteristics with general boundary value conditions and non-local initial data. A regular solution to the problem with known methods is constructed here. The uniqueness of the solution to the problem is proved by the method of energy integrals. This uses the theory of non-negative quadratic forms. The existence of a solution to the problem is proved by reducing the problem to Fredholm integral equations of the second kind. In this case, the method of Green’s function and potential is used. |
| first_indexed | 2024-03-10T10:47:01Z |
| format | Article |
| id | doaj.art-9e4eed37f1d049e8a625b360b6584aa5 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T10:47:01Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-9e4eed37f1d049e8a625b360b6584aa52023-11-21T22:30:11ZengMDPI AGAxioms2075-16802021-06-0110211010.3390/axioms10020110Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary ConditionsAbdukomil Risbekovich Khashimov0Dana Smetanová1Department of Higher Mathematics, Statistics and Econometry, Faculty of Accounting and Auditing, Tashkent Finance Institute, A. Temur 60A, Tashkent 100000, UzbekistanDepartment of Informatics and Natural Sciences, Faculty of Technology, Institute of Technology and Business in České Budějovice, Okružní 10, 370 01 Ceské Budějovice, Czech RepublicThe article considers third-order equations with multiple characteristics with general boundary value conditions and non-local initial data. A regular solution to the problem with known methods is constructed here. The uniqueness of the solution to the problem is proved by the method of energy integrals. This uses the theory of non-negative quadratic forms. The existence of a solution to the problem is proved by reducing the problem to Fredholm integral equations of the second kind. In this case, the method of Green’s function and potential is used.https://www.mdpi.com/2075-1680/10/2/110third order equations with multiple characteristicboundary conditionnonlocal problemuniqueness theoremFredholm integral equation of the second kindexistence theorem |
| spellingShingle | Abdukomil Risbekovich Khashimov Dana Smetanová Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary Conditions Axioms third order equations with multiple characteristic boundary condition nonlocal problem uniqueness theorem Fredholm integral equation of the second kind existence theorem |
| title | Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary Conditions |
| title_full | Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary Conditions |
| title_fullStr | Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary Conditions |
| title_full_unstemmed | Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary Conditions |
| title_short | Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary Conditions |
| title_sort | nonlocal problem for a third order equation with multiple characteristics with general boundary conditions |
| topic | third order equations with multiple characteristic boundary condition nonlocal problem uniqueness theorem Fredholm integral equation of the second kind existence theorem |
| url | https://www.mdpi.com/2075-1680/10/2/110 |
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