On solvability of the first boundary value problem for an odd order equation with changing time direction

We study the generalized and regular solvability of the first boundary value problem for an odd order equation with changing time direction. Using the nonstationary Galerkin method and the regularization method, the existence of a generalized solution and the unique regular solvability of the considered boundary value problem are proved. The error estimate for the nonstationary Galerkin method is also established.