We propose a method for the solution of the problem with inhomogeneous integral conditions for homogeneous differential-operator equations with abstract operator in a linear space H . For the righthand sides of the integral conditions from a 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 an example of application of the method to the solution of the ill-posed problem for the second-order partial differential equation in the time variable (in which the integral conditions are given) and, in general, an infiniteorder partial differential equation in the space variable.

Abstract:We propose a method of solving the problem with nonhomogeneous integral condition for homogeneous evolution equation with abstract operator in a linear space H. For right-hand side of the integral condition which belongs to the special subspace L ⊆ H, in which the vectors are represented using Stieltjes integrals over a certain measure, the solution of the problem is represented in the form of Stieltjes integral over the same measure.

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