一类四阶具有p-Laplacian算子微分方程周期解的存在性

Existence of Periodic Solutions for a Fourth-order p-Laplacian Differential Equation

本文主要利用Mawhin连续性定理,讨论了一类四阶带有变时滞的p-Lapcaian型泛函微分方程:(p(x″(t)))″+f(x′(t))+β(t)g(t,x(t),x(t-ι(t))),x′(t))=e(t)周期解的存在性,得到了方程周期解存在性的相关结论。这与已有的文献的结果不同,所考虑的方程更一般,从而所得的结果就更有广泛的意义。

In this paper, by means of Mawhin＇s continuation theorem, we study a kind of fourth-order p-Laplacian differential equation with delay as follows ：（φp（x″（f）））″＋f（x′（t））＋β（t）g（t,x（t）,x（t-τ（t））,x′（t））=e（t） A new result on the existence of periodic solution is obtained. Our results are different from the previous literatures, the equation considered is more general, which make the results have much more profound meaning.