On uniqueness of Neumann‐Tricomi problem in R 2

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 L [ u ] = f , d n u : = k ( y ) u x d y – u y d x |γ0 = = Ψ( s ) for a “general” function k ( y ), when r ( x, y ) is not necessarily zero and Γ 1 is of a more general form then in the papers of V. P. Egorov [6], [7].