On the existence of periodic solutions to p-Laplacian Rayleigh differential equation with a delay

In this paper, the authors study the existence of periodic solutions to a p-Laplacian Rayleigh differential equation with a delay as follows:(φp(y′(t)))′+f(y′(t))+g(y(t−τ(t)))=e(t),(φp(y′(t)))′+f(y′(t))+g(y(t−τ(t)))=e(t), where p>1p>1 is a constant, φp:R→R, φp(u)=|u|p−2uφp(u)=|u|p−2u, f,g,e,τ∈C(R,R)f,g,e,τ∈C(R,R), τ(t+T)≡τ(t)τ(t+T)≡τ(t) with τ(t)⩾0τ(t)⩾0, ∀t∈[0,T]∀t∈[0,T], and e(t+T)≡e(t)e(t+T)≡e(t), T>0T>0 is a constant. By using Mawhin's continuation theorem, some new results are obtained.