本文将Ф-有界变差函数理论与Kurzweil方程理论结合起来,首次给出了Ф-变差稳定性概念,讨论了Kurzweil方程Ф-有界变差解的稳定性,建立了Ф-界变差解Ф-变差稳定性和渐近Ф-变差稳定性的Ljapunov型定理。这些结果是对Kurzweil方程有界变差解变差稳定性的本质推广。
In this paper, the bounded Ф-variation function and the generalized ordinary differential equation are unified, the concept of Ф-variational stability is established and the stability of the bounded Ф-variation solutions to Kurzweil equations is discussed. The Ljapunov type theorems for Ф-variational stability and asymptotically Ф-variational stability of the bounded Ф-variation solutions are established. These results are an essential generalization of variation stability of bounded variation solutions to Kurzweil equations.