In this paper, we propose new sufficient conditions for stability of solutions of systems of Volterra linear integral equations and systems of linear integro-differential Volterra equations. Solution stability conditions for systems of Volterra linear integral equations are studied with perturbed right hand sides of the equations. These new sufficient conditions are expressed in terms of logarithmic norms of matrices consisting of coefficients of equations and derivatives of their kernels. For Volterra integro-differential equations we also provide sufficient conditions for stability of solutions when the initial conditions are perturbed.

中文翻译：

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Volterra 积分方程组解的稳定性

在本文中，我们提出了 Volterra 线性积分方程组和线性积分微分 Volterra 方程组解稳定性的新充分条件。利用方程右侧的扰动研究了 Volterra 线性积分方程组的解稳定性条件。这些新的充分条件用矩阵的对数范数来表示，该矩阵由方程系数及其核的导数组成。对于 Volterra 积分微分方程，我们还为初始条件受到扰动时解的稳定性提供了充分的条件。