Geodesic
The existence of solutions to an inhomogeneous higher order differential equation in the Schwartz space
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 4, pp. 454-459 
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) no. 4, pp. 454-459. http://geodesic.mathdoc.fr/item/JMAG_2020_16_4_a3/
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     title = {The existence of solutions to an inhomogeneous higher order differential equation in the {Schwartz} space},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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