Jehad Alzabut

Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis

By employing the contraction mapping principle and applying Gronwall-Bellmans inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.

Almost periodic solutions for an impulsive delay Nicholson's blowflies model

By means of the contraction mapping principle and Gronwall-Bellmans inequality, we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay Nicholsons blowflies model. The main results are illustrated by an example.

On almost periodic solutions for an impulsive delay logarithmic population model

By employing the contraction mapping principle and applying the Gronwall-Bellman inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solutions for an impulsive delay logarithmic population model. An example with its numerical simulations has been provided to demonstrate the feasibility of our results.

Positive almost periodic solutions for a delay logarithmic population model

By utilizing the continuation theorem of coincidence degree theory, we shall prove that a delay logarithmic population model has at least one positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result.

On existence of a globally attractive periodic solution of impulsive delay logarithmic population model

In this paper, it is shown that a logarithmic population model which is governed by impulsive delay differential equation has a globally attractive periodic solution.

Almost periodic dynamics of a discrete Nicholson’s blowflies model involving a linear harvesting term

We consider a discrete Nicholson’s blowflies model involving a linear harvesting term. Under appropriate assumptions, sufficient conditions are established for the existence and exponential convergence of positive almost periodic solutions of this model. To expose the effectiveness of the main theorems, we support our result by a numerical example.MSC:39A11.

On the Impulsive Delay Hematopoiesis Model with Periodic Coefficients

In this paper we shall consider the nonlinear impulsive delay hematopoiesis model p0(t) = β(t) 1 + pn(t−mω) − γ(t)p(t), t 6= tk, p(t+k ) = (1 + bk)p(tk), k ∈ N = {1, 2, . . .}, where n,m ∈ N, β(t), γ(t) and 0 0. We prove that the solutions are bounded and persist. The persistence implies the survival of the mature cells for long term. By means of the continuation theorem of coincidence degree, we prove the existence of a positive periodic solution p(t). We also establish some sufficient conditions for the global attractivity of p(t). These conditions imply the absence of any dynamic diseases in the mammal. Moreover, we obtain some sufficient conditions for the oscillation of all positive solutions about the positive periodic solution p(t). These conditions lead to the prevalence of the mature cells around the periodic solution. Our results extend and improve some well known theorems in the literature for the autonomous case without impulse. An example is considered to illustrate the main results.

Banach contraction principle for cyclical mappings on partial metric spaces

We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilić et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.MSC:47H10, 54H25.

Existence of Periodic Solutions of a Type of Nonlinear Impulsive Delay Differential Equations with a Small Parameter

Abstract The Banach fixed point theorem is used to prove the existence of a unique ω periodic solution of a new type of nonlinear impulsive delay differential equation with a small parameter.

Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives

AbstractWe state and prove new generalized Lyapunov-type and Hartman-type inequalities for a conformable boundary value problem of order α∈(1,2]