A priori bounds and nodal properties for periodic solutions to a class of ordinary differential equations (Q1206974)

The equation (1) \(x''(t)+b^ 2x(t)=g(x(t)\), \(x'(t)\), \(x''(t))\) is considered, where \(0\neq b\in R\), \(g(0,0,0)=0\). First the author proves a uniqueness result for the initial value problem associated with (1), having \(x(0)=x'(0)=0\). Second the author demonstrates the existence of periodic solutions of (1) for all periods in certain intervals and he proves that solutions of (1) with sufficiently small periods remain bounded.