Asymptotic behaviors of nonlinear neutral impulsive delay differential equations with forced term

Abstract

In this paper, we study the asymptotic behavior of solutions of a class of nonlinear neutral impulsive delay differential equations with forced term of the form $$\left\{\begin{array}{lll}[x(t)+c(t)x(t-\tau)]' +p(t)f(x(t-\delta))=q(t),& t\geq t_0, t\neq t_k,\\ x(t_k)=b_kx(t_k^-)+(1-b_k)\int_{t_k-\delta}^{t_k}p(s+\delta)f(x(s))ds\\ \qquad +(b_k-1)\int_{t_k}^\infty q(s)ds,& k\in{\mathbf{Z_+}}\end{array}\right.$$ Sufficient conditions are obtained for every solution of the equations that tends to a constant as t → ∞.