Limearized oscillations for odd-order neutral delay differential equations with asymptotic periodic coefficients

摘要

In this paper, we prove that, under appropriate hypotheses, the odd-order nonlinear neutral delay differential equation formula(ell.) has the same oscillatory character as the associated linear equation with periodic coefficients formula(ell.). (E) Our method is based on the establishment of a new comparison theorem for the Oscillation of Eq.(E). Hence we prove that the parameter set such that Eq.(E)has A nonoscillatory solution is closed in certain metric space, and avoid the difficulty To set the necessary and sufficient condition for the oscillation of Eq.(E).