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.

中文翻译：

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积分微分方程参数问题的适定性

摘要 积分微分方程参数问题近似为加载微分方程参数问题。积分微分方程的带参数问题的适定性是根据加载微分方程的带参数问题的适定性来建立的。获得了原始问题和近似问题的定性属性之间的相互关系，并设置了对它们的解决方案之间差异的估计。给出了带参数加载微分方程的一种新的通用解，并描述了其性质。加载微分方程的参数问题被简化为相对于引入的一般解的任意向量的线性代数方程组。