On the conditions for the solvability of boundary-value problems for a high-order equation with a discontinuous coefficient

Abstract

The paper considers a boundary value problem for the high-order Lavrent'ev-Bitsadze equation. Necessary and sufficient conditions for the uniqueness of the solution are found. When substantiating the existence, the problem of "small denominators" arises. Sufficient conditions for the separability of the "small denominator" from zero are found. An example of a boundary value problem not solvable by the Fourier method is given, in the cases rectangle with integer side measurements.