On Some Generalizations of Properties of the Lowndes Operator and their Applications to Partial Differential Equations of High Order

In this work we proved a composition of Lowndes' operator with differential operators of the high order, particularly, with iterated Bessel differential singular operator. Examples on applications of the proved properties to partial differential equations of the fourth and high order with singular coefficients were showed. By applying the proved theorems, explicit formulas of the solutions of considered problems were constructed.