一类二阶中立型微分差分方程周期解的存在性(英文)

Existence of Periodic Solutions to a Class of Second-order Neutral Differential Difference Equations

考虑如下二阶中立型微分差分方程的边值问题 :x(t-τ) - x(t-τ) + f (t,x(t) ,x(t-τ) ,x(t- 2τ) ) =0x(0 ) =x(2 kτ) ,x(0 ) =x(2 kτ)其中 k是任意给定的正整数 ,τ为正实数 .利用含有偏差变元的变分结构及临界点理论 ,作者给出了判定上述方程存在非平凡周期解的判定准则 .

by means of variational structure and critical P Oint theory, we give some criteria for the existence of periodic solutions to a Class of second-order neutral differential difference equations as the followin G type(t-τ)-x(t-τ)+f(t,x(t),x(t-τ),x(t-2τ))=0With the boundary value conditionX(0)=x(2kτ), (0)=(2kτ)Where k is a given positive integer and τ is a positive number.=