Show that the Riemann function for a general hyperbolic PDE in canonical form is unique. That is, prove that the problem

$$ R_{xy} - (aR)_x - (bR)_y + cR = 0 $$ with $$ \begin{aligned} &R_x = bR \qquad\text{on}\qquad y = y_0 \\ &R_y = aR \qquad\text{on}\qquad x = x_0 \\ &R(x_0, y_0) = 1 \end{aligned} $$

has a unique solution.

I tried to imitate approaches with Dirichlet, Neumann but they don't work. Any help appreciated!


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