Аннотация:The application of the method of spectral isolation of singularities for construct- ing a solution of a boundary value problem for an irregularly degenerate first-order elliptic differential operator with analytic coefficients in a rectangle necessitates solving a sequence of boundary value problems for degenerate first-order ordinary differential equations with analytic coefficients on a closed interval with a large parameter multiplying the unknown function. For the fundamental solution system of these equations and for the Green functions of this sequence of problems, estimates of their behavior as the parameter tends to infinity are obtained. The solution of the boundary value problem for an elliptic differential operator having analytic co- efficients and degenerating in one variable (y) is constructed as a Poisson series—a series in eigenfunctions of the limit operator with coefficients analytic in y. This paper generalizes the results previously obtained for similar equations with second-order degeneracy to the case of first-order degeneracy.
