Estimations of a Differential Operator in Spectral Parameter Problems for Elliptic Equations with Discontinuous Nonlinearities
The basic boundary value problems for semilinear equations of elliptic type with a spectral parameter and discontinuous nonlinearity are considered in a bounded domain with a sufficiently smooth boundary. The parameter values for which the corresponding problem has the nonzero solution are called ei...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2010-06-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Online Access: | http://mi.mathnet.ru/eng/vsgtu800 |
| _version_ | 1818420975471951872 |
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| author | D. K. Potapov |
| author_facet | D. K. Potapov |
| author_sort | D. K. Potapov |
| collection | DOAJ |
| description | The basic boundary value problems for semilinear equations of elliptic type with a spectral parameter and discontinuous nonlinearity are considered in a bounded domain with a sufficiently smooth boundary. The parameter values for which the corresponding problem has the nonzero solution are called eigenvalues. The existence of eigenvalue problem solutions for equations of elliptic type with discontinuous nonlinearities is considered in this paper. Estimations of the differential operator are obtained for these problems. |
| first_indexed | 2024-12-14T13:03:00Z |
| format | Article |
| id | doaj.art-f19d2661e27f4b38aa0d8d7f5d40e011 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-14T13:03:00Z |
| publishDate | 2010-06-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-f19d2661e27f4b38aa0d8d7f5d40e0112022-12-21T23:00:23ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812010-06-015(21)26827110.14498/vsgtu800Estimations of a Differential Operator in Spectral Parameter Problems for Elliptic Equations with Discontinuous NonlinearitiesD. K. PotapovThe basic boundary value problems for semilinear equations of elliptic type with a spectral parameter and discontinuous nonlinearity are considered in a bounded domain with a sufficiently smooth boundary. The parameter values for which the corresponding problem has the nonzero solution are called eigenvalues. The existence of eigenvalue problem solutions for equations of elliptic type with discontinuous nonlinearities is considered in this paper. Estimations of the differential operator are obtained for these problems.http://mi.mathnet.ru/eng/vsgtu800 |
| spellingShingle | D. K. Potapov Estimations of a Differential Operator in Spectral Parameter Problems for Elliptic Equations with Discontinuous Nonlinearities Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| title | Estimations of a Differential Operator in Spectral Parameter Problems for Elliptic Equations with Discontinuous Nonlinearities |
| title_full | Estimations of a Differential Operator in Spectral Parameter Problems for Elliptic Equations with Discontinuous Nonlinearities |
| title_fullStr | Estimations of a Differential Operator in Spectral Parameter Problems for Elliptic Equations with Discontinuous Nonlinearities |
| title_full_unstemmed | Estimations of a Differential Operator in Spectral Parameter Problems for Elliptic Equations with Discontinuous Nonlinearities |
| title_short | Estimations of a Differential Operator in Spectral Parameter Problems for Elliptic Equations with Discontinuous Nonlinearities |
| title_sort | estimations of a differential operator in spectral parameter problems for elliptic equations with discontinuous nonlinearities |
| url | http://mi.mathnet.ru/eng/vsgtu800 |
| work_keys_str_mv | AT dkpotapov estimationsofadifferentialoperatorinspectralparameterproblemsforellipticequationswithdiscontinuousnonlinearities |