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

摘要

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⩾t0,x(tk+)=Ik(x(tk)),k=1,2,….Our results improve the known results in the literature.