Oscillation criteria for first-order impulsive differential equations with positive and negative coefficients

Some sufficient conditions are obtained for oscillation of all solutions of the first-order impulsive differential equation with positive and negative coefficients [ x ( t ) - R ( t ) x ( t - r ) ] ′ + P ( t ) x ( t - τ ) - Q ( t ) x ( t - σ ) = 0 , τ ⩾ σ > 0 , t ⩾ t 0 , x ( t k + ) = I k ( x ( t k ) ) , k = 1 , 2 , … . Our results improve the known results in the literature.