一类三阶多时滞p-Laplacian方程周期解的存在性

The Existence of Perodic Solutions for a Class of Third-Order p-Laplacian Equations with Delays

利用重合度理论中的延拓定理,研究如下一类三阶p-Laplacian微分方程:(φp((x(t)-cx(t-σ))″))′+f1(x(t))x′(t)+f2(x′(t))x″(t)+g(t,x(t),x(t-τ1(t)),x′(t-τ2(t)))=e(t)的T-周期解问题,得到了上述方程存在T-周期解的若干新结果,所得结论与方程多个变滞量有关.

In this paper,using the continuation theorem of coincidence degree,a type of third order p-Laplacian equation with delays（φp（（x（t）-cx（t-σ））″））′＋f1（x（t））x′（t）＋f2（x′（t））x″（t）＋g（t,x（t）,x（t-τ1（t））,x′（t-τ2（t）））=e（t）is considered.Some new results for T-periodic solutions to such equation are obtained.The conclusions are related to the equation of multiple bariable delays.