ASYMPTOTIC AND OSCILLATORY BEHAVIOR OF HIGHER ORDER QUASILINEAR DELAY DIFFERENTIAL EQUATIONS

In the paper, we offer such generalization of a lemma due to Philos (and partially Staikos), that yields many applications in the oscillation theory. We present its disposal in the comparison theory and we establish new oscillation criteria for n-th order delay differential equation (E) (r(t) [x ' (t)]gamma)((n-1)) + q(t)x(gamma) (tau(t)) = 0. The presented technique essentially simplifies the examination of the higher order differential equations