Existence theorem for periodic solutions of higher order nonlinear differential equations (Q1378740)

The authors prove the existence of a \(T\)-periodic solution of the equation \[ x^{(m)}+ a_{m-1}x^{(m-1)}+ \cdots+ a_1x'+ g(t,x,x',\dots, x^{(m)})= f(t), \] where \(f(t)\equiv f(t+ T)\). Unlike in the majority of similar papers, the nonlinearity \(g\) depends explicitly on the highest derivative \(x^{(m)}\).