THE CLASSICAL SOLUTION OF THE MIXED PROBLEM FOR THE EQUATION WITH INVOLUTION AND MULTIPOINT BOUNDARY CONDITIONS
In this paper a classical solution of the mixed problem for a first order differential equation with involution in the case of two-point boundary conditions of general form is obtained. In the case of symmetric potential solution is found explicitly. For the case arbitrary potential using the received refined asymptotic formulas for the eigenvalues and eigenfunctions of the corresponding spectral problem, the application of the Fourier method is substantiated. We used techniques, which allow to transform a series representing the formal solution on Fourier method, and to prove the possibility of his term by term differentiation. At the same time on the initial data of the problem minimum requirements are imposed.