Elliptic problems with nonlocal potential arising in models of nonlinear optics

DOI10.1134/S0001434619050109zbMath1433.35045OpenAlexW2953967365WikidataQ127578733 ScholiaQ127578733MaRDI QIDQ2334912

A. B. Muravnik

Publication date: 8 November 2019

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434619050109

zbMATH Keywords

elliptic problemsdifferential-difference equationsnonlocal potential

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25)

Related Items (17)

Elliptic equations with translations of general form in a half-space ⋮ Hyperbolic differential-difference equations with nonlocal potentials ⋮ Elliptic differential-difference equations with nonlocal potentials in a half-space ⋮ Half-plane differential-difference elliptic problems with general-kind nonlocal potentials ⋮ Classical solutions of hyperbolic differential-difference equations with several nonlocal terms ⋮ Classical solutions of hyperbolic differential-difference equations in a half-space ⋮ A classical solution to a hyperbolic differential-difference equation with a translation by an arbitrary vector ⋮ Strongly elliptic differential-difference equations with mixed boundary conditions in a bounded domain ⋮ Classical solutions of a multidimensional hyperbolic differential-difference equation with shifts of various directions in the potentials ⋮ On one Cauchy problem for a hyperbolic differential-difference equation ⋮ On global classical solutions of hyperbolic differential-difference equations ⋮ Classical solutions of hyperbolic equations with nonlocal potentials ⋮ On non-uniqueness of recovering Sturm-Liouville operators with delay ⋮ Iso-bispectral potentials for Sturm-Liouville-type operators with small delay ⋮ Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling ⋮ Global classical solutions of some two-dimensional hyperbolic differential-difference equations ⋮ Inverse problems for Dirac operators with constant delay: uniqueness, characterization, uniform stability

Cites Work

• Asymptotic properties of solutions of the Dirichlet problem in the half-plane for differential-difference elliptic equations
• Diffractive patterns in a nonlinear optical two-dimensional feedback system with field rotation
• Bifurcation of periodic solutions for nonlinear parabolic functional differential equations arising in optoelectronics
• On the half-plane Dirichlet problem for differential-difference elliptic equations with several nonlocal terms
• On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations
• Elliptic functional differential equations and applications
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