Problem with integral conditions for differential-operator equation

Анотація

We propose a method of solving the problem with inhomogeneous integral conditions for homogeneous differential-operator equation with abstract operator in a linear space H. For right-hand sides of the integral conditions which belong to the special subspace L⊆H, in which the vectors are represented in the form of Stieltjes integrals with respect to certain measures, the solution of the problem is represented in the form of Stieltjes integrals with respect to the same measures. We give the example of applying the method to solving the ill-posed problem for the second order partial differential equation in time variable (in which the integral conditions are given) and, generally, an infinite order partial differential equation in spatial variable.