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Using Mawhin’s continuation theorem we obtain some existence results of periodic solutions for a type of p-Laplacian neutral Liénard equation $$\left( {\phi _p \left( {\left( {x\left( t \right) - c\left( t \right)x\left( {t - \tau } \right)} \right)^\prime } \right)} \right)^\prime + f\left( {x\left( t \right)} \right)x'\left( t \right) + g\left( {x\left( {t - \gamma \left( t \right)} \right)} \right) = e\left( t \right).$$ It is worth noting that c(t) is no longer a constant which is different from the corresponding ones of past work.


In this paper, by using a fixed-point theorem in cones to study the boundary value problem for a class of quadratic mixed type of delay differential equations with eigenvalue, the sufficient condition of existence of their solutions is derived. The main results in this paper are the generalization and improvement of those existing ones.