On construction of the Riemann function for certain equation in \(N\)-dimensional space (Q1589062)

The Riemann function for the equation \[ \frac{\partial^nu} {\partial x_1 x_2\dots x_n}+ \sum_{k=1}^n \sum_{Q_n^k} a_{q_1\dots q_k} \frac{\partial^{n-k}u} {\partial x_{q_{k+1}\dots x_{q_n}}}= 0, \] where \(Q_n^k= \{(q_1,\dots, q_n)\mid 1\leq q_j \leq n\), \(q_1<\cdots< q_k\), \(q_{k+1}<\cdots< q_n\}\) and the coefficients are continuously differentiable, is defined as a solution of an integral equation. Under different conditions on the coefficients of the given equation, new variants of integral equations for constructing the Riemann function are proposed.