Boundary-value problems for second-order differential operators with nonlocal boundary conditions
In this paper, we study a second-order differential operator combining weighting integral boundary condition with another two-point boundary condition. Under certain conditions on the weighting functions, called regular and non regular cases, we prove that the resolvent decreases with respect to the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2007-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/56/abstr.html |
| _version_ | 1818988298018750464 |
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| author | Mohamed Denche Abderrahmane Meziani |
| author_facet | Mohamed Denche Abderrahmane Meziani |
| author_sort | Mohamed Denche |
| collection | DOAJ |
| description | In this paper, we study a second-order differential operator combining weighting integral boundary condition with another two-point boundary condition. Under certain conditions on the weighting functions, called regular and non regular cases, we prove that the resolvent decreases with respect to the spectral parameter in $L^{p}(0,1)$, but there is no maximal decrease at infinity for $p>1$. Furthermore, the studied operator generates in $L^{p}(0,1) $, an analytic semi group for $p=1$ in the regular case, and an analytic semi group with singularities for $p>1$, in both cases, and for $p=1$, in the non regular case only. The obtained results are then used to show the correct solvability of a mixed problem for parabolic partial differential equation with non regular boundary conditions. |
| first_indexed | 2024-12-20T19:20:21Z |
| format | Article |
| id | doaj.art-38506dbc976c498ebbe970ea30ad9bb4 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T19:20:21Z |
| publishDate | 2007-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-38506dbc976c498ebbe970ea30ad9bb42022-12-21T19:29:01ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-04-01200756121Boundary-value problems for second-order differential operators with nonlocal boundary conditionsMohamed DencheAbderrahmane MezianiIn this paper, we study a second-order differential operator combining weighting integral boundary condition with another two-point boundary condition. Under certain conditions on the weighting functions, called regular and non regular cases, we prove that the resolvent decreases with respect to the spectral parameter in $L^{p}(0,1)$, but there is no maximal decrease at infinity for $p>1$. Furthermore, the studied operator generates in $L^{p}(0,1) $, an analytic semi group for $p=1$ in the regular case, and an analytic semi group with singularities for $p>1$, in both cases, and for $p=1$, in the non regular case only. The obtained results are then used to show the correct solvability of a mixed problem for parabolic partial differential equation with non regular boundary conditions.http://ejde.math.txstate.edu/Volumes/2007/56/abstr.htmlGreen's functionregular and non regular boundary conditionssemi group with singularitiesweighted mixed boundary conditions. |
| spellingShingle | Mohamed Denche Abderrahmane Meziani Boundary-value problems for second-order differential operators with nonlocal boundary conditions Electronic Journal of Differential Equations Green's function regular and non regular boundary conditions semi group with singularities weighted mixed boundary conditions. |
| title | Boundary-value problems for second-order differential operators with nonlocal boundary conditions |
| title_full | Boundary-value problems for second-order differential operators with nonlocal boundary conditions |
| title_fullStr | Boundary-value problems for second-order differential operators with nonlocal boundary conditions |
| title_full_unstemmed | Boundary-value problems for second-order differential operators with nonlocal boundary conditions |
| title_short | Boundary-value problems for second-order differential operators with nonlocal boundary conditions |
| title_sort | boundary value problems for second order differential operators with nonlocal boundary conditions |
| topic | Green's function regular and non regular boundary conditions semi group with singularities weighted mixed boundary conditions. |
| url | http://ejde.math.txstate.edu/Volumes/2007/56/abstr.html |
| work_keys_str_mv | AT mohameddenche boundaryvalueproblemsforsecondorderdifferentialoperatorswithnonlocalboundaryconditions AT abderrahmanemeziani boundaryvalueproblemsforsecondorderdifferentialoperatorswithnonlocalboundaryconditions |