Problem with Integral Conditions for Differential-Operator Equation

We propose a method for the solution of the problem with inhomogeneous integral conditions for homogeneousdifferential-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...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2015-07, Vol.208 (3), p.267-276
Main Authors: Kalenyuk, P. I., Kuduk, G., Kohut, I. V., Nytrebych, Z. M.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We propose a method for the solution of the problem with inhomogeneous integral conditions for homogeneousdifferential-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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-015-2444-z