On quick oscillations in functional equations with deviating arguments (Q761610)

For the functional equation \(L_ ny(t)+H(t,y(g(t))=f(t)\), \(n\geq 2\), where \[ L_ n=\frac{1}{p_ n(t)}\frac{d}{dt}\frac{1}{p_{n- 1}(t)}\frac{d}{dt}...\frac{d}{dt}\frac{1}{p_ 1(t)}\frac{d}{dt}\frac{\cdot}{p_ 0(t)} \] sufficient conditions are found to ensure that a solution is either quickly oscillating or else it is nonoscillatory. Both canonical and noncanonical forms of \(L_ n\) are studied.