We present the definitions of two new Lyapunov functionals. These functionals are applied to establish sufficient conditions guaranteeing the asymptotic stability, uniform stability, and boundedness of solutions of certain nonlinear Volterra integrodifferential equations of the first order. The obtained results improve and extend known results available from literature. We also propose examples to show the applicability of our results and illustrate them. By using MATLAB-Simulink, we clearly show, in particular cases, the behavior of orbits of the analyzed Volterra integrodifferential equations.

中文翻译：

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非线性Volterra积分微分方程解的渐近稳定性、一致稳定性和有界性

我们给出了两个新的 Lyapunov 泛函的定义。应用这些函数来建立保证某些非线性 Volterra 一阶积分微分方程解的渐近稳定性、一致稳定性和有界性的充分条件。获得的结果改进和扩展了从文献中可获得的已知结果。我们还提出了一些例子来展示我们的结果的适用性并说明它们。通过使用 MATLAB-Simulink，我们可以在特定情况下清楚地显示所分析的 Volterra 积分微分方程的轨道行为。