On boundary value problems with normal high-order derivatives on characteristics

Abstract

A loaded Volterra integral equation has been obtained that connects the boundary values of the Goursat problem and the values of the normal derivatives of the desired function on characteristics of arbitrarily high order. In this case, the boundary values of the required function are determined up to a certain set of arbitrary constants. On the basis of the obtained result, sufficient conditions for the solvability of a problem with linear combinations of normal derivatives of different orders given on the characteristics are obtained. An estimate is obtained for the number of arbitrary constants on which the solution of the specified problem may depend.