Geodesic
Elliptic Problems with Nonlocal Potential Arising in Models of Nonlinear Optics
Matematičeskie zametki, Tome 105 (2019) no. 5, pp. 747-762

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

The Dirichlet problem in the half-plane for strong elliptic differential-difference equations with nonlocal potentials is considered. The classical solvability of this problem is proved, and the integral representation of this classical solution by a Poisson-type relation is constructed.
Keywords: differential-difference equations, elliptic problems, nonlocal potential. 
@article{MZM_2019_105_5_a8,
     author = {A. B. Muravnik},
     title = {Elliptic {Problems} with {Nonlocal} {Potential} {Arising} in {Models} of {Nonlinear} {Optics}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {747--762},
     publisher = {mathdoc},
     volume = {105},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a8/}
}
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A. B. Muravnik. Elliptic Problems with Nonlocal Potential Arising in Models of Nonlinear Optics. Matematičeskie zametki, Tome 105 (2019) no. 5, pp. 747-762. http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a8/