Boundary value problem for a model differential equation with involution in a rectangular domain

In the present work, the solvability of a classical boundary value problem for a degenerate partial differential equation of the second order with an involutive deviation of the argument of the form (-x) in a rectangular domain is first established and studied. The existence and uniqueness theorems of the regular solution are proved for the studied problem. Some conditions on the coefficients, when fulfilling which the problem has a singular solution, are set. The question of solvability of the problem in the required class of functions by the method of separation of variables is reduced to the solvability of the corresponding ordinary differential equation with involutive deviation of the argument, the solution of which is constructed by the method of differentiation.