  There is studied problem on existence of solutions to non-homogeneous
differential equation of higher even order. Similar problem arises while
studying soliton and soliton-like solutions to partial differential equations
of integrable type.
  By means of Fourier transform and theory of pseudodifferential operators
there is proved the theorem on necessary and sufficient conditions on existence
of solutions to linear non-homogeneous differential equation of higher even
order in the Schwartz space.
