In this paper the uniqueness problem of the Cha-for y≠0)is considered.The domain D is bounded(?)by three curves showing in the figure,where T_1 and T_2are characteristics defined by the equation dx~2+Kdy~2=O,T_3 is a continuous curve.Let the coordinate of P be(Xo/yo)and the minimum and maximum abscissas ofT_3 be x_1 and x_2.When y<0,let 1+2(K/k_y)=f(y)and(?)Let in(n=0,1,2)be the least positive roots of the following equations:(?)Where δ=0 or 1 according to x_0+2Y(?) Finally,let y_1=0 if f(y)>0 for all y0≤y<0,otherwise let y1 be the upperbound of values y in the interval yo≤y<0 satisfying f(y)<0.Theorem.If y1<0 and there exists a positive numberεand an integer n(n=0,1,2)such that the following relation holds for yo≤y≤y1:(?)and if u is a quasi-regular solution which vanishes on T_2+T_3,then u=0 in D.The example for gas dynamical problem shows that this theorem is better than theresult of [1] and [2].The method of proof of the theorem is to consider the sum of the energy integral(?)dxdy=0 and the zero integral(?)(Pu~2)+
