CLASSIFICATION OF SOLUTIONS OF SECOND ORDER IMPULSIVE NEUTRAL DELAY DIFFERENTIAL EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS

摘要

This paper is focused on the following nonlinear impulsive neutral delay differential equation with positive and negative coefficients [r(t)(x(t) + c(t)x(t - τ))']' + p(t)f(x(t - δ) - q(t)g(x(t - σ)) = 0, x(t_k) = I_k(x(t_k~-)), x'(t_k) = J_k(x'(t_k~-)), k = 1,2,3,..., where 0 ≤ t_0 < t_1 < t_2 < … < t_k … with lim sum from k→∞ t_k = ∞. For this equation, oscillation criteria are established.