In this paper, a class of impulsive difference equations with time-varying delays is considered. By establishing an impulsive delay difference inequality, some sufficient conditions ensuring all solutions either oscillate or tend to zero are obtained. An example is given to illustrate the feasibility of the obtained result. AMS Subject Classifications: 34K15, 34K10.

Differential equations arise in many real world problems such as physics, population dynamics, ecology, biological systems, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. Much has been done under the assumption that the state variables and system parameters change continuously. However, one may easily visualize situations in nature where abrupt changes such...

In this paper, we prove the existence of solutions of initial value problems for nth order nonlinear impulsive integro-differential equations of mixed type on an infinite interval with an infinite number of impulsive times in Banach spaces. Our results are obtained by introducing a suitable measure of noncompactness.

A desirable property of any space-time used to model a physically plausible scenario is that the evolution of the Einstein’s equations is well posed i.e. the initial value problem has a unique solution. Space-times whose metrics are at least C, which guarantees the existence of unique geodesics, fall within the context of the Cosmic Censorship Hypothesis of Penrose (1979). The hypothesis states...

Respiratory Syncytial Virus (RSV) is an acute respiratory infection that infects millions of children and infants worldwide. Recent research has shown promise for the development of a vaccine, with a range of vaccine types now in clinical trials or preclinical development. We extend an existing mathematical model with seasonal transmission to include vaccination. We model vaccination both as a ...

In this paper, we study semi-analytical methods entitled Homotopy pertourbation method (HPM) to solve fuzzy impulsive fractional differential equations based on the concept of generalized Hukuhara differentiability. At the end first of Homotopy pertourbation method is defined and its properties are considered completely. Then econvergence theorem for the solution are proved and we will show tha...

In this paper, we study mixed boundary value problem for secondorder impulsive differential equations with a parameter. By using critical point theory, several new existence results are obtained. This is one of the first times that impulsive boundary value problems are studied by means of variational methods.

In this paper, a prey predator impulsive mathematical model of integrated pest management is established, in which infected prey and predator (natural enemy) are released impulsively. By using the Floquet’s theory for impulsive differential equations, small-amplitude perturbation methods and comparison techniques, we investigate the local and global stability of the susceptible pest-eradication...