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运用Mawhin 重合度拓展定理研究了一类广义平均曲率Liénard 方程( x′1+x′2)′+f(x(t))x′(t)+β(t)g(x(t-τ(t)))=e(t)。周期解存在性与唯一性问题，得到了周期解存在性与唯一性的相关新结果。“,”By using the coincidence degree theory, some new results were established, on the exist-ence and uniqueness of T-periodic solutions for a kind of prescribed mean curvature Liénard equation of the form ( x′1+x′2)′+f(x(t))x′(t) +β(t)g(x(t-τ(t))) =e(t).