On the existence of periodic solutions to \(p\)-Laplacian Rayleigh differential equation with a delay (Q854086)

By using Mawhin's continuation theorem, the authors study the existence of periodic solutions of the \(p\)-Laplacian Rayleigh differential equation with delay \[ (\varphi_p(y'(t))'+f(y'(t))+g(y(t-\tau(t)))=e(t), \] where \(p>1\) is a constant, \(\varphi_p:\mathbb{R}\rightarrow \mathbb{R},\varphi_p(u)=| u| ^{p-2}u, f, g,e, \tau\in C(\mathbb{R},\mathbb{R}),\tau(t+T)\equiv\tau(t)\) with \(\tau(t)\geq 0\) \(\forall t\in [0, T]\), \(e(t+T)\equiv e(t)\) and \(T>0\) is a constant.