Existence Of Periodic Positive Solutions Research Articles

Positive periodic solutions for revisited Nicholson's blowflies equation with iterative harvesting term

Nicholson's blowflies differential equation is one of the famous equations in the field of population dynamics. The first steps of the apparition of this equation began in the 1950s with the Nicholson experiments on the sheep blowfly Lucilia cuprina, the hot topic in Australia at that time and since then it has drawn more and more attention of many researchers. The main purpose of the current study is to investigate the existence of periodic positive solutions for Nicholson's blowflies differential equation with an iterative harvesting function by using Schauder's fixed point theorem. Finally, an example is employed to illustrate the effectiveness of our results.

Existence of periodic positive solutions to nonlinear Lotka-Volterra competition systems

We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, On positive periodic solution of Lotka-Volterra competition systems with deviating arguments, Proc. Amer. Math. Soc. 134 (2006), 2967-2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature.

Existence of periodic positive solutions for a competitive system with two parameters

In this paper, a nonlinear competitive system with two parameters is considered. By constructing a curve , we divide the parameters space into two disjoint subsets and . Furthermore, we obtain the sufficient conditions on the existence of the positive periodic solutions in and on by using the method of upper and lower solutions and the degree theory. More specifically, for the competitive system, there are at least two positive periodic solutions for , at least one positive periodic solution for , and no positive periodic solution for .

The Existence of Positive Periodic Solution for a Class of Functional Differential Equation with Multi-Delays

We discuss the existence of periodic positive solution of one kind of multiple time-delay functional differential equations with the cone theory and fixed index method in semi-order Banach space of nonlinear functional analysis.

Existence of Periodic Positive Solutions for Abstract Difference Equations

We will consider the existence of multiple positive periodic solutions for a class of abstract difference equations by using the well‐known fixed point theorem (due to Krasnoselskii).

Existence of positive periodic solution of a neutral impulsive delay predator–prey system

Sufficient conditions are obtained for the existence of periodic positive solution of the neutral impulsive delay predator–prey system. This is the first time that positive solution for impulsive delay predator–prey system is obtained by using the theory of coincidence degree. Our results in this paper indicate that under the appropriate linear periodic impulsive perturbations, the neutral impulsive delay predator–prey system preserves the original periodicity of the neutral nonimpulsive delay predator–prey system.

Periodicity and attractivity for a rational recursive sequence

In this paper, the existence of periodic positive solution and the attractivity are investigated for the rational recursive sequencexn+1=(A+axn−k)/(b+xn−1), whereA, a andb are real numbers,k andl are nonnegative integer numbers.

Mathematische Behandlung ernes Modells der Haemodialyse

AbstractIn this paper a simple mathematical model for the process of hemodialysis is presented. This model is based on a system of two linear differential equations of first order with partly discontinuous coefficients that describe the time‐development of the concentrations of a certain toxin (like urea) in the intra‐ and extracellular part of the human body. The main result is the existence of periodic positive solutions of this system under the natural assumption that the generation of the toxin and its removal by hemodialysis are periodic processes. These periodic positive solutions are also computed numerically for a realistic choice of the coefficients of the modelling differential equations.