New results of periodic solutions for a class of delay Rayleigh equation (Q731981)

The author investigates the existence and uniqueness of the periodic solution of the Rayleigh equation with two delays \[ x''(t)+f(t,x'(t))+g_1(t,x(t-\tau_1))+g_2(t,x(t-\tau_2))=e(t), \] where \(\tau_1,\tau_2\geq 0\) and the functions \(f,g_1,g_2\in C(\mathbb{R}^2,\mathbb{R})\) and \(e\in C(\mathbb{R},\mathbb{R})\) are \(T\)-periodic with respect to the variable \(t\) and such that \(f(t,0)=0\) for all \(t\in\mathbb{R}\). To prove the existence result the author uses Mawhin's continuation theorem. An illustrative example is also provided.