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Problem with integral condition for evolution equation

Kalenyuk P. I., Kuduk G., Kohut I. V., Nytrebych Z. M.

Journal of Mathematics and Applications

2015

Vol. 38

71--76

We propose a method of solving the problem with non-homogeneous 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 H ⊆ L, 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.