Multipoint problem for higher-order parabolic equations in a parallelepiped

We study the well-posedness of a problem for a Petrovskii-parabolic equation with coefficients depending on the space coordinates and with multipoint conditions with respect to the time variable. We establish conditions for the existence and uniqueness of the classical solution of the problem. For the proof of the existence of a solution of the problem, the method of divided differences is used. We prove a metric-type theorem on lower bounds for the small denominators that appear in the construction of the solution.