Oscillating periodic solutions of third order nonlinear differential equations (Q1205194)

The nonlinear differential equation under consideration has the form (1) \(x^{(3)}=pg(x)+q\), where \(p,q\in C({\mathbf R}_ +,{\mathbf R})\), \(g\in C({\mathbf R},{\mathbf R})\), and \(p\), \(q\) are \(\omega\)-periodic. Sufficient conditions are obtained for the existence of solutions \(x(t)\) of (1) which are both oscillatory at \(\infty\) and \(\omega\)-periodic.