Well-posedness of problem with parameter for an integro-differential equation

A. T. Assanova, E. А. Bakirova, Gulmira K. Vassilina

2020

Data confidence 70 medium

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Abstract

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.