In this paper, the regularization method of S. A. Lomov is generalized to integro-differential equations with rapidly oscillating coefficients and with a rapidly oscillating right-hand side. The main goal of the work is to reveal the influence of the oscillating components on the structure of the asymptotics of the solution of this problem. The case of coincidence of the frequencies of a rapidly oscillating coefficient and a rapidly oscillating inhomogeneity is considered. In this case, only the identical resonance is observed in the problem. Other cases of the relationship between frequencies can lead to so-called non-identical resonances, the study of which is nontrivial and requires the development of a new approach. It is supposed to study these cases in our further work.

中文翻译：

---

具有快速振动系数和快速振动非均质性的奇摄动偏积分微分方程的柯西问题的渐近解

在本文中，将SA Lomov的正则化方法推广到系数快速波动且右侧快速波动的积分微分方程。这项工作的主要目的是揭示振荡分量对解决该问题的渐近结构的影响。考虑快速振荡系数和快速振荡不均匀性的频率一致的情况。在这种情况下，在该问题中仅观察到相同的共振。频率之间关系的其他情况可能会导致所谓的“不相同的共振”，其研究是不平凡的，需要开发一种新的方法。应该在进一步的工作中研究这些案例。