Harmonic and subharmonic solutions for suplinear Duffing equation with delay (Q519478)

The authors consider second order differential equations of the form \[ x''(t)+g(x(t-\tau))=p(t), \] where \(g:\mathbb{R}\to\mathbb{R}\) is locally Lipschitz continuous, \(\tau>0\) is a constant, \(p:\mathbb{R}\to\mathbb{R}\) is continuous and periodic. An additional hypothesis is that the nonlinear map \(g\) is superlinear. Using a fixed point theorem for twist mappings, the existence of harmonic and subharmonic solutions is proved.