A linear boundary value problem for a system of composite partial differential equations

A two-variable system of first-order partial differential equations is investigated which has, in the region under consideration, one family of real characteristics and two families of imaginary characteristics. A general linear boundary value problem for the system is studied. It is proved that if a certain condition is imposed on the coefficients in the boundary conditions, there is only a finite number of linearly independent solutions of the homogeneous problem and of the adjoint homogeneous problem. A formula for the index of the above problem is derived and a necessary and sufficient condition for the solvability of the inhomogeneous problem is obtained in terms of the homogeneous adjoint problem.