Positive solutions of higher order ordinary differential equations with general nonlinearities (Q1588417)

The authors study positive solutions to ordinary differential equations of the form \[ X^{(n)}\pm p(t)f(x)= 0,\tag{1} \] with \(n\geq 2\), \(p(t)\), \(f(x)\) are continuous, \(f(x)> 0\) for \(x>0\), \(p(t)\geq 0\) for \(t\geq t_0\). The existence of positive solutions to equation (1) is discussed for the general nonlinearity case.