Periodic solution to p-Laplacian neutral Liénard type equation with variable parameter

Abstract

Abstract 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.