Oscillation and a class of linear delay differential equations

Abstract

The differential equation u ( m ) ( t ) + p ( t ) u ( g ( t ) ) = 0 {u^{(m)}}(t) + p(t)u(g(t)) = 0 . where P is one-signed, is broken into four cases, according to the parity of m and the sign of p. In each case, an analysis is given of the effect g can have on oscillation properties, and oscillation and nonoscillation criteria are given.