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Mat. Zametki, 2019, Volume 105, Issue 5, Pages 747–762 (Mi mz11992)  

This article is cited in 4 scientific papers (total in 4 papers)

Elliptic Problems with Nonlocal Potential Arising in Models of Nonlinear Optics

A. B. Muravnikab

a "Sozvezdie"
b Peoples' Friendship University of Russia, Moscow

Abstract: 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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 5-100
НШ-4479.2014.1
Russian Foundation for Basic Research 17-01-00401
This work was supported by the Ministry of Education and Science of the Russian Federation by the Program for Raising the Competitiveness of RUDN University “5-100” among the leading research centers of the world for 2016–2020. This work was also supported by the Presidential Program under grant NSh-4479.2014.1 and by the Russian Foundation for Basic Research under grant 17-01-00401.


DOI: https://doi.org/10.4213/mzm11992

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English version:
Mathematical Notes, 2019, 105:5, 734–746

Bibliographic databases:

UDC: 517.956
Received: 15.03.2018
Revised: 19.08.2018

Citation: A. B. Muravnik, “Elliptic Problems with Nonlocal Potential Arising in Models of Nonlinear Optics”, Mat. Zametki, 105:5 (2019), 747–762; Math. Notes, 105:5 (2019), 734–746

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Muravnik A.B., “Half-Plane Differential-Difference Elliptic Problems With General-Kind Nonlocal Potentials”, Complex Var. Elliptic Equ.  crossref  mathscinet  isi
    2. V N. Zaitseva, “Global classical solutions of some two-dimensional hyperbolic differential-difference equations”, Differ. Equ., 56:6 (2020), 734–739  crossref  mathscinet  zmath  isi
    3. V N. Zaitseva, “On global classical solutions of hyperbolic differential-difference equations”, Dokl. Math., 101:2 (2020), 115–116  crossref  isi
    4. Zaitseva N.V., “Classical Solutions of Hyperbolic Differential-Difference Equations With Several Nonlocal Terms”, Lobachevskii J. Math., 42:1 (2021), 231–236  crossref  mathscinet  zmath  isi  scopus
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