三阶p-Laplacian中立型泛函微分方程的周期解

Periodic Solutions for Three-Order p-Laplacian Neutral Functional Differential Equation

利用Mawhin重合度理论,研究一类三阶p-Laplacian中立型泛函微分方程[φp(x(t)-∑n j=1cjx(t-r))″]′+f(x(t))x′(t)+α(t)g(x(t))+∑n j=1βj(t)g(x(t-γj(t)))=p(t)周期解的存在性,得到了这类方程至少存在一个T周期解的充分条件.

Using Mawhin＇s coincidence degree theorem,the authors studied the existence of periodic solutions for three-order p-Laplacian neutral functional differential equation[φpx（t）-∑n j=1cjx（t-rj）） ″]′＋f（x（t））x′（t）＋α（t）g（x（t））＋∑n j=1βj（t）g（x（t-γj（t）））=p（t）suggesting that there exists one sufficient condition,at least,for the existence of T-periodic solutions.