Abstract
A problem with parameter for an integro-differential equation is approximated by a problem with parameter for a loaded differential equation. The well-posedness of a problem with parameter for the integro-differential equation is established in the terms of the well-posedness of a problem with parameter for the loaded differential equation. A mutual relationship between the qualitative properties of original and approximate problems is obtained, and the estimates for differences between their solutions are set. A new general solution to the loaded differential equation with parameter is presented, and its properties are described. The problem with parameter for the loaded differential equation is reduced to a system of linear algebraic equations with respect to the arbitrary vectors of a general solution introduced. The system’s coefficients and right-hand sides are computed by solving the Cauchy problems for ordinary differential equations.
Funding source: Ministry of Education and Science of the Republic of Kazakhstan
Award Identifier / Grant number: AP05132455
Award Identifier / Grant number: AP05132486 and AP05131220
Funding statement: This research is supported by Ministry of Education and Science of the Republic of Kazakhstan Grants AP05132455, AP05132486 and AP05131220.
Acknowledgements
The authors thank the referee for his/her careful reading of the manuscript and useful suggestions which allowed us to improve the present paper.
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