We introduce the classes $H,H_δ,S_δ$ of linear systems of partial differential equations. Some symmetric polynomials in the roots of the characteristic equations of the systems for these classes are nontrivial and its allow power estimates from below. Based on the metric approach and theory of symmetric polynomials we show that almost all systems of partial differential equations with constants coefficients (with respect to the Lebesgue measure in the space
spanned by system coefficients) belong to the introduced classes.

The problem with two multiple nodes on the selected variable $t$ and periodicity conditions in other coordinates $x_1, . . . , x_p$ for linear systems of partial differential equations belonging to the described classes $H,H_δ,S_δ$ is investigated. The conditions of solvability problem in the spaces of smooth vector functions with exponential behavior of Fourier vector-coefficients are established. It is proved that estimates for small denominators provided the existence of the solution of the problem are performed for almost all (respect to the Lebesgue measure and the Hausdorff fractal measure) of the values of the second interpolation node for linear systems from the classes $H,H_δ,S_δ$.

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