On uniqueness of Neumann-Tricomi problem in R2

We consider the equation of mixed type (k(y) ? 0 whenever y ? 0) in a region G which is bounded by the curves: A piecewise smooth curve Γ lying in the half-plane y > 0 which intersects the line y = 0 at the points A(-1, 0) and B(0, 0). For y < 0 by a piecewise smooth curve Γ through A which meets the characteristic of (1) issued from B at the point P and the curve Γ which consists of the portion PB of the characteristic through B. We obtain sufficient conditions for the uniqueness of the solution of the problem Lu] = f, d_nu: = k(y)u_xdy – u_ydx|γ0 = = Ψ(s) for a “general” function k(y), when r(x, y) is not necessarily zero and Γ₁ is of a more general form then in the papers of V. P. Egorov 6], 7].