OSCILLATION OF NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATION WITH SEVERAL COEFFICIENTS

摘要

In this article, we show that the oscillation of all solutions to the neutral equation [x(t)-R(t)N(x(t-κ))]'+(sum from i=1 to n of (P_i(t)F_i(x(t-τ_i))-(sum from i=1 to m of (Q_j(t)G_j(t-σ_j)) = 0 is implied by the oscillation of all solutions to the linear equation [x(t)-rx(x(t-κ))]'+(sum from i=1 to n of (p_ix(x(t-τ_i))-(sum from i=1 to m of (q_jx(t-σ_j)) = 0 In these equations, R, P_i, Q_j are positive and continuous functions, and κ, τ_i, σ_j are positive constants that represent delays.