On the existence of periodic solutions to a \(p\)-Laplacian Rayleigh equation (Q1032726)

The existence of periodic solutions of the \(p\)-Laplacian Rayleigh equation \[ (\varphi_p(x'(t)))' + f(x'(t)) + g(x(t-\tau(t))) = e(t) \] is studied, where \(\varphi_p(s) = |s|^{p-2}s\), \(p>1\), \(\varphi_q = \varphi_p^{-1}\), \(\frac{1}{p} + \frac{1}{q} = 1\) and \(f\), \(g\), \(e\) and \(\tau\) are continuous functions with \(e\) and \(\tau\) being \(T\)-periodic. Sufficient conditions are obtained for the existence of at least one \(T\)-periodic solution by means of the generalised Mawhin's continuation theorem.