scholarly journals Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Yuzhen Mi
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fourier Series ◽  
Small Perturbation ◽  
Homoclinic Solution ◽  
Fourier Series Expansion ◽  
Volterra System ◽  
Perturbation Theorem ◽  
Expansion Technique ◽  
The Fixed Point Theorem

This paper investigates Lotka-Volterra system under a small perturbationvxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux),uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that nearμ=0the system has a generalized homoclinic solution exponentially approaching a periodic solution.

scholarly journals Diffusion in Semiconductors by Using Fourier Series Expansion Technique

2014 ◽  
Vol 11 (2) ◽  
pp. 90-97
Author(s):  
M El-Adawi ◽  
S Abdel-Ghany ◽  
S Shalaby
Keyword(s):  
Fourier Series ◽  
Diffusion Equation ◽  
Mass Balance ◽  
Series Expansion ◽  
Theoretical Approach ◽  
Balance Equation ◽  
Concentration Function ◽  
Fourier Series Expansion ◽  
Mass Balance Equation ◽  
Expansion Technique

Doping by diffusion is still one of acceptable and important methods that have essential technological applications. A theoretical approach to study diffusion in semi-conductors is introduced. The diffusion equation together with Fick's law and mass balance equation are solved to obtain the concentration function and the mass penetration depth using Fourier Series expansion technique. Doping of indium, phosphorus, gallium and Arsenic in Silicon as illustrative examples are given.

scholarly journals An Almost Periodic Lasota-Wazewska Dynamic Model on Time Scales

2018 ◽  
pp. 17-32
Author(s):  
Zhijian Yao
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Positive Solution ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Iterative Sequence ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
The Fixed Point Theorem

This paper deals with almost periodicity of Lasota-Wazewska dynamic equation on time scales. By applying a method based on the fixed point theorem of decreasing operator, we establish sufficient conditions for the existence of a unique almost periodic positive solution. We also give iterative sequence which converges to almost periodic positive solution. Moreover, we investigate the exponential stability of almost periodic solution by means of Gronwall inequality. Our study unifies differential and difference equations.

From homoclinics to quasi-periodic solutions for ordinary differential equations

2015 ◽  
Vol 145 (5) ◽  
pp. 1091-1114
Author(s):  
Changrong Zhu
Keyword(s):  
Functional Analysis ◽  
Periodic Solution ◽  
Fixed Point ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Homoclinic Solution ◽  
Unperturbed System ◽  
Perturbed System ◽  
Hyperbolic Fixed Point ◽  
Parameter Values

We consider the quasi-periodic solutions bifurcated from a degenerate homoclinic solution. Assume that the unperturbed system has a homoclinic solution and a hyperbolic fixed point. The bifurcation function for the existence of a quasi-periodic solution of the perturbed system is obtained by functional analysis methods. The zeros of the bifurcation function correspond to the existence of the quasi-periodic solution at the non-zero parameter values. Some solvable conditions of the bifurcation equations are investigated. Two examples are given to illustrate the results.

scholarly journals The Unique Periodic Solution of Abel’s Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Ni Hua
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Lyapunov Function ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
The Fixed Point Theorem

In this paper, the existence of a periodic solution for Abel’s differential equation is obtained first by using the fixed-point theorem. Then, by constructing the Lyapunov function, the uniqueness and stability of the periodic solution of the equation are obtained.

Design of Turbomachinery Blading in Transonic Flows by the Circulation Method

1992 ◽  
Vol 114 (1) ◽  
pp. 141-146
Author(s):  
T. Q. Dang
Keyword(s):  
Fourier Series ◽  
Transonic Flow ◽  
Three Dimensional ◽  
Fourier Series Expansion ◽  
Main Task ◽  
Design Technique ◽  
Transonic Flows ◽  
Circulation Method ◽  
Expansion Technique ◽  
Volume Method

The newly developed three-dimensional design technique for turbomachinery blading based on the circulation method has been successfully extended into the transonic flow regime. The main task involves replacing the classical Fourier series expansion technique by a finite-volume method. Calculations were carried out for the design of infinitely thin cascaded blades in transonic flows, including shocked and shock-free cascaded blades.

scholarly journals Fourier Approximation for Integral Equations on the Real Line

2009 ◽  
Vol 2009 ◽  
pp. 1-10
Author(s):  
S. M. Hashemiparast ◽  
H. Fallahgoul
Keyword(s):  
Integral Equation ◽  
Periodic Solution ◽  
Fourier Series ◽  
Integral Equations ◽  
Real Line ◽  
Finite Interval ◽  
High Accuracy ◽  
Fourier Series Expansion ◽  
Fourier Approximation ◽  
The Real

Based on Guass quadradure method a class of integral equations having unknown periodic solution on the real line is investigated, by using Fourier series expansion for the solution of the integral equation and applying a process for changing the interval to the finite interval (; 1), the Chebychev weights become appropriate and examples indicate the high accuracy and very good approximation to the solution of the integral.

scholarly journals Existence of Positive Periodic Solutions for a Class ofn-Species Competition Systems with Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Peilian Guo ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
The Fixed Point Theorem

By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class ofn-species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect.

scholarly journals Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

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