中文摘要：

研究了一类二阶时滞微分方程周期解的存在性与多解性。假设f具有某种对称性并且是奇函数,如果f在零点和无穷远点渐近线性增长时,应用临界点理论和Z2伪几何指标理论,得到了上述方程关于周期解存在性与多重性的一些新结果。

英文摘要：

The existence and multiplicity of the periodic solutions to a class of second order delay differential equations are discussed.Provided that f is odd and possesses a certain symmetric property,by using the critical point and the geometrical pseudo index theory,some new achievements of the multiple periodic solutions to the above-mentioned equations are made on condition that f grows asymplotically linear both at zero and at infinity.