Geodesic
On the Dirichlet problem for differential-difference elliptic equations in a~half-plane
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 3, Tome 60 (2016), pp. 102-113

Voir la notice de l'article provenant de la source Math-Net.Ru

The Dirichlet problem is considered in a half-plane (with continuous and bounded boundaryvalue function) for the model elliptic differential-difference equation $$ u_{xx}+au_{xx}(x+h,y)+u_{yy}=0,\qquad|a|1. $$ Its solvability is proved in the sense of generalized functions, the integral representation of the solution is constructed, and it is proved that everywhere but the boundary hyperplane this solution satisfies the equation in the classic sense as well. 
@article{CMFD_2016_60_a3,
     author = {A. B. Muravnik},
     title = {On the {Dirichlet} problem for differential-difference elliptic equations in a~half-plane},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {102--113},
     publisher = {mathdoc},
     volume = {60},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2016_60_a3/}
}
TY  - JOUR
AU  - A. B. Muravnik
TI  - On the Dirichlet problem for differential-difference elliptic equations in a~half-plane
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2016
SP  - 102
EP  - 113
VL  - 60
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2016_60_a3/
LA  - ru
ID  - CMFD_2016_60_a3
ER  - 
%0 Journal Article
%A A. B. Muravnik
%T On the Dirichlet problem for differential-difference elliptic equations in a~half-plane
%J Contemporary Mathematics. Fundamental Directions
%D 2016
%P 102-113
%V 60
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2016_60_a3/
%G ru
%F CMFD_2016_60_a3
A. B. Muravnik. On the Dirichlet problem for differential-difference elliptic equations in a~half-plane. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 3, Tome 60 (2016), pp. 102-113. http://geodesic.mathdoc.fr/item/CMFD_2016_60_a3/