Kurzweil方程的Φ-变差稳定性

Φ-variational Stability for Kurzweil Equations

本文将Φ-有界变差函数理论与Kurzweil方程理论结合起来,首次给出了Φ-变差稳定性概念,讨论了Kurzweil方程Φ-有界变差解的稳定性,建立了Φ-界变差解Φ-变差稳定性和渐近Φ-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.