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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2020, Volume 16, Number 4, Pages 454–459
DOI: https://doi.org/10.15407/mag16.04.454 (Mi jmag766) 		 
The existence of solutions to an inhomogeneous higher order differential equation in the Schwartz space

Valerii Samoilenko, Yuliia Samoilenko

Taras Shevchenko National University of Kyiv, 60 Volodymyrska St., Kyiv, 01601, Ukraine
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DOI: https://doi.org/10.15407/mag16.04.454
Abstract: The paper deals with the problem of the existence of solutions to an inhomogeneous linear differential equation of higher even order. The problem arises while studying soliton and soliton-like solutions to partial differential equations of integrable type. The theorem on necessary and sufficient conditions of the existence of solutions to the differential equation in the Schwartz space of rapidly decreasing functions is proved by means of theory of pseudodifferential operators.
Key words and phrases: existence of solutions, higher order differential equations, the Schwartz space of rapidly decreasing functions, pseudodifferential operators.
Received: 15.09.2019
Revised: 14.01.2020
Bibliographic databases:
Document Type: Article
MSC: 35A01, 35J30, 47G30
Language: English
Citation: Valerii Samoilenko, Yuliia Samoilenko, “The existence of solutions to an inhomogeneous higher order differential equation in the Schwartz space”, Zh. Mat. Fiz. Anal. Geom., 16:4 (2020), 454–459
Citation in format AMSBIB
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\by Valerii~Samoilenko, Yuliia~Samoilenko
\paper The existence of solutions to an inhomogeneous higher order differential equation in the Schwartz space
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2020
\vol 16
\issue 4
\pages 454--459
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\crossref{https://doi.org/10.15407/mag16.04.454}
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