scholarly journals Mean-Square Almost Periodic Solutions for Impulsive Stochastic Host-Macroparasite Equation on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Pan Wang ◽  
Qingmei Lin ◽  
Yongkun Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scales ◽  
Banach Fixed Point Theorem ◽  
Mean Square ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Inequality Technique ◽  
Bellman’S Inequality

We consider an impulsive stochastic host-macroparasite equation on time scales. By use of the Banach fixed point theorem and Gronwall-Bellman’s inequality technique on time scales, we obtain the existence and exponential stability of mean-square almost periodic solutions for the host-macroparasite equation on time scales. Finally, we give an example to illustrate the feasibility of our results.

Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay

2019 ◽  
Vol 20 (01) ◽  
pp. 2050003
Author(s):  
Xiao Ma ◽  
Xiao-Bao Shu ◽  
Jianzhong Mao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Infinite Delay ◽  
Almost Periodic Solutions ◽  
Almost Periodic

In this paper, we investigate the existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay in Hilbert space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. In the end, we give an example to illustrate our main results.

scholarly journals Almost Periodic Solutions for Second Order Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Wang ◽  
Lan Li
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Almost Periodic Functions ◽  
Dynamic Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions

We firstly introduce the concept and the properties ofCmalmost periodic functions on time scales, which generalizes the concept of almost periodic functions on time scales and the concept ofC(n)-almost periodic functions. Secondly, we consider the existence and uniqueness of almost periodic solutions for second order dynamic equations on time scales by Schauder’s fixed point theorem and contracting mapping principle. At last, we obtain alternative theorems for second order dynamic equations on time scales.

ALMOST PERIODICITY IN AN IMPULSIVE LOGISTIC EQUATION WITH INFINITE DELAY

2008 ◽  
Vol 01 (03) ◽  
pp. 355-360 ◽  
Author(s):  
CHUNHUA FENG ◽  
ZHENKUN HUANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Logistic Equation ◽  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic

By employing a fixed point theorem in cones, this paper investigates the existence of almost periodic solutions for an impulsive logistic equation with infinite delay. A set of sufficient conditions on the existence of almost periodic solutions of the equation is obtained.

scholarly journals Almost periodic solutions of a discrete Lotka-Volterra model via exponential dichotomy theory

2021 ◽  
Vol 7 (3) ◽  
pp. 3788-3801
Author(s):  
Lini Fang ◽  
◽  
N'gbo N'gbo ◽  
Yonghui Xia
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Exponential Dichotomy ◽  
Exponential Convergence ◽  
Volterra Model ◽  
Banach Fixed Point Theorem ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
The Difference ◽  
Positive Almost Periodic Solutions

<abstract><p>In this paper, we consider a discrete non-autonomous Lotka-Volterra model. Under some assumptions, we prove the existence of positive almost periodic solutions. Our analysis relies on the exponential dichotomy for the difference equations and the Banach fixed point theorem. Furthermore, by constructing a Lyapunov function, the exponential convergence is proved. Finally, a numerical example illustrates the effectiveness of the results.</p></abstract>

scholarly journals Existence and Uniqueness of Almost Periodic Solutions for Neural Networks with Neutral Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Min Xu ◽  
Zengji Du ◽  
Kaige Zhuang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic

A class of neural networks system with neutral delays is investigated. The existence and uniqueness of almost periodic solution for the system are obtained by using fixed point theorem; we extend some results in the references.

scholarly journals The analysis of some special results of a Lasota–Wazewska model with mixed variable delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramazan Yazgan ◽  
Osman Tunç
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Time Varying ◽  
Differential Inequalities ◽  
Almost Periodic ◽  
Variable Delays ◽  
Pseudo Almost Periodic ◽  
Mixed Variable

AbstractThis study is about getting some conditions that guarantee the existence and uniqueness of the weighted pseudo almost periodic (WPAP) solutions of a Lasota–Wazewska model with time-varying delays. Some adequate conditions have been obtained for the existence and uniqueness of the WPAP solutions of the Lasota–Wazewska model, which we dealt with using some differential inequalities, the WPAP theory, and the Banach fixed point theorem. Besides, an application is given to demonstrate the accuracy of the conditions of our main results.

scholarly journals Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

2018 ◽  
Vol 104 (118) ◽  
pp. 23-41 ◽  
Author(s):  
Marko Kostic
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Fixed Point Theorems ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
Sectorial Operators ◽  
Almost Sectorial Operators ◽  
Fractional Relaxation ◽  
Asymptotically Almost Periodic

We analyze asymptotically almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. As auxiliary tools, we use subordination principles, fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularities at zero. Our results are well illustrated and seem to be not considered elsewhere even for fractional relaxation equations with almost sectorial operators.

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