Quasi-periodic solutions for an asymmetric oscillation (Q2832520)

The authors consider the equation of a forced asymmetric oscillator of the type NEWLINE\[NEWLINEx''+ax^+ -bx^- =f(t),NEWLINE\]NEWLINE where \(x^+\) and \(x^-\) denote the positive and negative parts of a real number and \(a\neq b\) are positive constants. When \(f(t)\) is periodic the boundedness of all solutions has been discussed in previous papers. In the present paper the theory is extended to the quasi-periodic case. More precisely, it is assumed that \(f(t)=F(\omega_1 t,\dots ,\omega_N t)\) where the frequency vector \((\omega_1 ,\dots ,\omega_N )\) satisfies a Diophantine condition and the function \(F\) is smooth enough.