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), where p > 1 is a constant, ϕp :R → R, ϕp(u) = |u|p−2u, f, g, e, τ ∈ C(R,R), τ(t + T ) ≡ τ(t) with τ(t) 0, ∀t ∈ [0,T ], and e(t + T ) ≡ e(t), T >0 is a constant. By using Mawhin’s continuation theorem, some new results are obtained. © 2006 Elsevier Inc. All rights reserved.