Geodesic
The existence of solutions to an inhomogeneous higher order differential equation in the Schwartz space
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020), pp. 454-459

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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. 
@article{JMAG_2020_16_a3,
     author = {Valerii Samoilenko and Yuliia Samoilenko},
     title = {The existence of solutions to an inhomogeneous higher order differential equation in the {Schwartz} space},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {454--459},
     publisher = {mathdoc},
     volume = {16},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2020_16_a3/}
}
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Valerii Samoilenko; Yuliia Samoilenko. The existence of solutions to an inhomogeneous higher order differential equation in the Schwartz space. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020), pp. 454-459. http://geodesic.mathdoc.fr/item/JMAG_2020_16_a3/