Abstract
This paper is concerned with a non-autonomous impulsive neutral integro-differential equation with time-varying delays. We establish a novel singular delay integro-differential inequality, which enables us to derive several sufficient criteria on the positive invariant set, global attracting set and stability. An example is given to demonstrate the efficiency of proposed r
Highlights
Due to the plentiful dynamical behaviors, integro-differential equations with delays have many applications in a variety of fields such as control theory, biology, ecology, medicine, etc [1, 2]
It worth noting that those results in previous literature [21]-[24] have only focused on the stability of the equilibrium point for autonomous impulsive neutral differential equations with delays
Based on the novel non-autonomous singular delay integro-differential inequality established in Section 3, we investigate the global attracting set and positive invariant set for (3), which have not been considered in [21, 24]
Summary
Due to the plentiful dynamical behaviors, integro-differential equations with delays have many applications in a variety of fields such as control theory, biology, ecology, medicine, etc [1, 2]. In [21], the exponential stability for impulsive neutral differential equations with finite delays has been studied by using differential inequality technique. In [24], authors studied the exponential stability for impulsive neutral integro-differential equations with delays by developing a singular integro-differential inequality. It worth noting that those results in previous literature [21]-[24] have only focused on the stability of the equilibrium point for autonomous impulsive neutral differential equations with delays. Motivated by the above discussion, we will investigate the asymptotic behaviors of solutions for a non-autonomous impulsive neutral integro-differential equation with time-varying delays in this. In this paper, the presented singular integro-differential inequality is non-autonomous, which means the coefficients are time varying.
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