Geodesic
Boundary-value problems for second-order differential operators with nonlocal boundary conditions
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $p greater than 1$. 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 $p greater than 1$, 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.
Classification : 47E05, 35K20
Keywords: Green's function, regular and non regular boundary conditions, semi group with singularities, weighted mixed boundary conditions 
@article{EJDE_2007__2007__a125,
     author = {Denche, Mohamed and Meziani, Abderrahmane},
     title = {Boundary-value problems for second-order differential operators with nonlocal boundary conditions},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a125/}
}
TY  - JOUR
AU  - Denche, Mohamed
AU  - Meziani, Abderrahmane
TI  - Boundary-value problems for second-order differential operators with nonlocal boundary conditions
JO  - Electronic Journal of Differential Equations
PY  - 2007
VL  - 2007
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a125/
LA  - en
ID  - EJDE_2007__2007__a125
ER  - 
%0 Journal Article
%A Denche, Mohamed
%A Meziani, Abderrahmane
%T Boundary-value problems for second-order differential operators with nonlocal boundary conditions
%J Electronic Journal of Differential Equations
%D 2007
%V 2007
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a125/
%G en
%F EJDE_2007__2007__a125
Denche, Mohamed; Meziani, Abderrahmane. Boundary-value problems for second-order differential operators with nonlocal boundary conditions. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a125/