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Article

A Boundary Value Problem for Noninsulated Magnetic Regime in a Vacuum Diode

1
Departamento de Matemáticas, Universidad Nacional de Colombia, sede Bogotá 2, Bogotá, Colombia
2
Institute of Mathamatics and Information Technologies, Irkutsk State University, Irkutsk 664003, Russia
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(4), 617; https://doi.org/10.3390/sym12040617
Received: 15 March 2020 / Revised: 3 April 2020 / Accepted: 4 April 2020 / Published: 14 April 2020
In this paper, we study the stationary boundary value problem derived from the magnetic (non) insulated regime on a plane diode. Our main goal is to prove the existence of non-negative solutions for that nonlinear singular system of second-order ordinary differential equations. To attain such a goal, we reduce the boundary value problem to a singular system of coupled nonlinear Fredholm integral equations, then we analyze its solvability through the existence of fixed points for the related operators. This system of integral equations is studied by means of Leray-Schauder’s topological degree theory. View Full-Text
Keywords: relativistic Vlasov-Maxwell system; magnetic insulation; singular boundary value problem; Leray-Schauder degree theory relativistic Vlasov-Maxwell system; magnetic insulation; singular boundary value problem; Leray-Schauder degree theory
MDPI and ACS Style

Rojas, E.M.; Sidorov, N.A.; Sinitsyn, A.V. A Boundary Value Problem for Noninsulated Magnetic Regime in a Vacuum Diode. Symmetry 2020, 12, 617. https://doi.org/10.3390/sym12040617

AMA Style

Rojas EM, Sidorov NA, Sinitsyn AV. A Boundary Value Problem for Noninsulated Magnetic Regime in a Vacuum Diode. Symmetry. 2020; 12(4):617. https://doi.org/10.3390/sym12040617

Chicago/Turabian Style

Rojas, Edixon M., Nikolai A. Sidorov, and Aleksandr V. Sinitsyn. 2020. "A Boundary Value Problem for Noninsulated Magnetic Regime in a Vacuum Diode" Symmetry 12, no. 4: 617. https://doi.org/10.3390/sym12040617

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