Problem with integral condition for evolution equation

Abstract

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.