Solvability of linear non-homogeneous higher order differential equation in the Schwartz space

TL;DR

This paper investigates the conditions under which higher even order linear non-homogeneous differential equations have solutions within the Schwartz space, providing a comprehensive solvability criterion.

Contribution

It establishes necessary and sufficient conditions for the existence of solutions to these differential equations in the Schwartz space.

Findings

Proved a theorem on solvability conditions in Schwartz space

Identified necessary and sufficient conditions for solutions

Enhanced understanding of differential equations in functional spaces

Abstract

There is studied problem on solvability of linear non-homogeneous differential equation of higher even order. There is proved the theorem on necessary and sufficient conditions on existence of solutions to the equation in the Schwartz space.