Oscillation of second order self-conjugate differential equation with impulses

In this paper, we investigate the oscillation of second-order self-conjugate differential equation with impulses(1) ( a ( t ) ( x ( t ) + p ( t ) x ( t - τ ) ) ′ ) ′ + q ( t ) x ( t - σ ) = 0 , t ≠ t k , t ⩾ t 0 , (2) x ( t k + ) = ( 1 + b k ) x ( t k ) , k = 1 , 2 , … , (3) x ′ ( t k + ) = ( 1 + b k ) x ′ ( t k ) , k = 1 , 2 , … , where a , p , q are continuous functions in [ t 0 , + ∞ ) , q ( t ) ⩾ 0 , a ( t ) > 0 , ∫ t 0 ∞ ( 1 / a ( s ) ) d s = ∞ , τ > 0 , σ > 0 , b k > - 1 , 0 < t 0 < t 1 < t 2 < ⋯ < t k < ⋯ and lim k → ∞ t k = ∞ . We get some sufficient conditions for the oscillation of solutions of Eqs. (1)–(3).