On the solutions of multi-dimensional arbitrary order differential equation with mixed senior partial derivative and power-law non-linearities

We study the solutions of a multi-dimensional differential equation of arbitrary order containing mixed senior partial derivative and power-law non-linearities on unknown function and its first derivatives. The method of functional separation of variables is applied for examining of this equation. The particular solutions of the equation under consideration are obtained. Some theorems which permit to decrease the order of this equation are proved.