一类二阶中立型泛函微分方程的无穷多个次调和周期解

Infinite Subharmonic Periodic Solutions to a Class of Second-order Neutral Differential Equations

本文通过变分原理和Z2不变群指标,得出了下述二阶中立型泛函微分方程存在无穷多个次调和周期解的充分条件(p(t)(μx′(t))+x′(t-τ)+μx′(t-2τ))′-q(t)x(t)+f(t,x(t),x(t-τ),x(t-2τ))=0,|μ|<1/2.

In this paper,by critical point and Z2- group index theory,we obtain infinite subharmonic periodic solutions to second-order nonlinear non-autonomous Sturm-Liouville neutral functional differential equations （p（t（μx′）（t））＋x′（t-τ）＋μx′（t-2τ））′-q（t）x（t）＋f（t,x（t）,x（t-τ）,x（t-2τ））=0,｜μ｜〈1/2.