Periodic Solutions to a Kind of Second Order Neutral Functional Differential Equation in the Critical Case

In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows:

$ {\left( {x{\left( t \right)} - cx{\left( {t - \tau } \right)}} \right)}^{{\prime \prime }} = g{\left( {t,x{\left( {t - \mu {\left( t \right)}} \right)}} \right)} + e{\left( t \right)}, $ {\left( {x{\left( t \right)} - cx{\left( {t - \tau } \right)}} \right)}^{{\prime \prime }} = g{\left( {t,x{\left( {t - \mu {\left( t \right)}} \right)}} \right)} + e{\left( t \right)},
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