Asymptotic behavior of solutions of nonlinear impulsive delay differential equations with positive and negative coefficients

This paper is concerned with the nonlinear impulsive delay differential equations with positive and negative coefficients equation(*){x′(t)+p(t)f(x(t−τ))−q(t)f(x(t−σ))=0,t≥t0,t≠tk,x(tk)=bkx(tk−)+(1−bk)(∫tk−τtkp(s+τ)f(x(s))ds−∫tk−σtkq(s+σ)f(x(s))ds),k=1,2,3,…. Sufficient conditions are obtained for every solution of equation (*) tending to a constant as t→∞t→∞.