Oscillation of nth order strongly noncanonical delay differential equations

Abstract The oscillatory properties of solutions to the n th order delay differential equations L n y ( t ) + p ( t ) y ( τ ( t ) ) = 0 , where L n is a disconjugate strongly noncanonical differential operator, p ( t ) > 0 , τ ( t ) ≤ t , and lim t → ∞ τ ( t ) = ∞ , are studied. The main idea is to show that, unlike Trench original, rather theoretical result, simple closed formulas appearing in an uniquely determined canonical representation of L n are possible, under one (mild) additional condition. As a consequence, new oscillation theorems for strongly noncanonical higher-order equations are formulated. Moreover, our results generalize even several ones obtained for n = 3 , 4 .