Oscillation criteria of certain even order nonlinear differential equation with piecewise constant argument (Q2858081)

The authors study even order-nonlinear differential equation with piecewise constant argument of the form NEWLINE\[NEWLINE(r(t)x^{(n)}(t))'+f(t,x([t]))=0,\tag{1}NEWLINE\]NEWLINE where \(n\) is an odd number, \(r(t)>0\) for \(t\geq 0\) and \(\int_0^{\infty}r^{-1}(t)dt=\infty\). In addition, \(xf(t,x)>0\) for \(x\neq 0\) and \(t\geq 0\). By applying the well-known Kiguradze's lemma, they establish three sufficient conditions for the oscillation of equation (1).