Boundary-value problems for second-order differential operators with nonlocal boundary conditions
Date
2007-04-17
Authors
Denche, Mohamed
Meziani, Abderrahmane
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Green's function, Regular and non regular boundary conditions, Semi group with singularities, Weighted mixed boundary conditions
Citation
Denche, M., & Meziani, A. (2007). Boundary-value problems for second-order differential operators with nonlocal boundary conditions. <i>Electronic Journal of Differential Equations, 2007</i>(56), pp. 1-21.
Rights
Attribution 4.0 International