Quasi-periodic solutions of a damped reversible oscillator at resonance (Q637047)

The paper deals with the differential equation \[ x''+a\,x^{+}-b\,x^{-}+\varphi (x)+f(x,x',t)=p(t), \] where \(a,b\in (0,\infty )\) are such that \(a\neq b\) and \(1/\sqrt {a}+1/\sqrt {b}=2/n\) for some \(n\in \mathbb {N},\) \(\varphi ,p\in C^2(\mathbb {R})\) and \(f\in C^2(\mathbb {R}^3).\) Moreover, \(p\) and \(f(x,y,.)\) are \(2\,\pi \)-periodic. The authors give conditions ensuring that there is \(\epsilon _0>0\) such that, for each \(\omega \in (n,n+\epsilon _0)\), the given equation has a solution of Mather type with rotation number \(\omega \).