Quasi-periodic solutions of a forced asymmetric oscillator at resonance

It is proved the existence of Aubry-Mather sets and infinitely many subharmonic solutions to an equation of the form $u''+a u^{+}-b u^{-} + \phi(u) = p(t)$, where $u^{+}= \max\{u,0\}, \; u^{-}=\max\{-u,0\}$, $\phi: {\bf R} \to {\bf R}$ is continuous, $p:[0,2\pi] \to {\bf R}$ is continuous and $2\pi$-periodic. We deal with the situation when $a\neq b$ are two positive constants satisfying $1/\sqrt{a}+1/\sqrt{b}=2/n \, (n \in {\bf N})$.