Method of solving Cauchy problem for inhomogeneous differential-operator equation

Анотація

We propose a method of solving the Cauchy problem for high order inhomogeneous equation with operator coefficients in a certain linear space. For the right-hand sides of the initial conditions and the equation, which are represented as Stieltjes integrals over a certain measure, the solution of the problem is represented as a sum of Stieltjes integrals over the same measure. We describe some applica­tions of the method for solving the Cauchy problem for inhomogeneous partial differential equations of infinite order in a spatial variable.