A problem with two nonlocal boundary conditions for a mixed type equation (Q1594370)

The mixed type equation \[ \text{sgn }y|y|^m u_{xx}+ u_{yy}= 0,\quad m>0\tag{1} \] is considered in the domain \(D\) bounded by the straight lines \(x= 0\) and \(x=1\) when \(y>0\) and by the characteristics of (1) when \(y< 0\). The authors formulate and prove solvability of a boundary value problem for (1) with nonlocal boundary conditions.