Boundedness in asymmetric oscillations at resonance in a critical situation (Q2102533)

In this paper, the second-order differential equation \[ x'' + a x^+ - b x^- + \varphi(x) = p(t) \] is considered, where \(x^+=\max\{x,0\}\), \(x^-=\max\{-x,0\}\), \(a\) and \(b\) are positive constants, and \(p\) is periodic. A sufficient condition for every solution to be bounded is established.