Essentially nonlocal boundary value problem for a certain partial differential equation (Q1585610)

The equation \[ \text{sgn }y|y|^m u_{xx}+ u_{yy}= 0,\quad m>0\tag{1} \] was considered in \(x\in (0,1)\), \(y\in \text{OC}\cup \text{AC}\), where OC and AC are characteristics of (1) passing through the points \(O(0,0)\), \(A(1,0)\), \(C(1/2,-((m+ 2)/4)^{2/(m+ 2)})\). The authors formulated a boundary value problem for (1) with nonlocal conditions at the boundary that include the operators of Riemann-Liouville type. The uniqueness result was proved.