dc.contributor.author Denche, Mohamed ( ) dc.contributor.author Meziani, Abderrahmane ( ) dc.date.accessioned 2021-08-06T13:39:47Z dc.date.available 2021-08-06T13:39:47Z dc.date.issued 2007-04-17 dc.identifier.citation Denche, M., & Meziani, A. (2007). Boundary-value problems for second-order differential operators with nonlocal boundary conditions. Electronic Journal of Differential Equations, 2007(56), pp. 1-21. en_US dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/14217 dc.description.abstract 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 Lp(0, 1), but there is no maximal decrease at infinity for p > 1. Furthermore, the studied operator generates in Lp(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. dc.format Text dc.format.extent 21 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Texas State University-San Marcos, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. dc.subject Green's function en_US dc.subject Regular and non regular boundary conditions en_US dc.subject Semi group with singularities en_US dc.subject Weighted mixed boundary conditions en_US dc.title Boundary-value problems for second-order differential operators with nonlocal boundary conditions en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License. dc.description.department Mathematics
﻿