Tricomi's problem for a second order system of equations (Q1907452)

By the integral equation method the author proves the unique solvability of the Tricomi problem for the system \[ W_{xx}+ yW_{yy}+ {1- n- k\over 2} W_y+ {n- k\over 2\sqrt{- y}} W_x= 0 \] in \(D\), where \(D\cap \{y> 0\}= \{y> 0\}\) and \(D\cap \{y< 0\}\) is bounded by the characteristics: \(x- 2\sqrt{- y}= 0\), \(x+ 2\sqrt{- y}= 1\) and \(y= 0\), and \(n, k\in \mathbb{N}\).