Existence of slow oscillations in functional equations (Q916860)

For the equation \(L_ ny(t)+H(t,y(t))=f(t)\) sufficient conditions are found to ensure that all proper solutions are slowly oscillating. The operator \(L_ n\) has the form \[ L_ n=\frac{1}{p_ n(t)}\frac{d}{dt}\frac{1}{p_{n-1}(t)}...\frac{d}{dt}\frac{1}{p_ 1(t)}\frac{d}{dt}\frac{\cdot}{p_ 0(t)}. \]