【摘要】 考虑时滞微分方程x′(t)=-f(x(t-1)),其中f∈C(R,R)是一个奇函数且满足xf(x)>0(x≠0).本文通过引进角速度函数以及应用移动直角三角形技巧,给出了上述方程至多有一个周期为4的Kaplan-Yorke型周期解的充分条件,首次改进了Nussbaum(1979)的唯一性结果.最后,本文还举例给出了定理的应用.更多还原

【Abstract】 Consider the following delay differential equation x′(t) =-f(x(t- 1)), where f ∈ C(R, R) is odd and satisfies xf(x) > 0 for x ≠ 0. By introducing the angular speed function and developing a novel technique, the moving triangle technique, we obtain sufficient conditions for the above equation to have at most one Kaplan-Yorke periodic solution with period 4. This is the first time to improve the uniqueness result obtained by Nussbaum in1979. Finally, an example is given to illustrate our results.更多还原