scholarly journals Some results on the existence of weak periodic solutions for quasilinear parabolic systems with L1 data

2022 ◽  
Vol 40 ◽  
pp. 1-15
Author(s):  
Abderrahim Charkaoui ◽  
Ghada Kouadri ◽  
Nour Eddine Alaa
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Reaction Diffusion ◽  
Parabolic Systems ◽  
Diffusion System ◽  
L1 Data ◽  
Quasilinear Parabolic

The aim of this paper is to prove the existence of weak periodic solution and super solution for M×M reaction diffusion system with L1 data and nonlinearity on the gradient. The existence is proved by the technique of sub and super solution and Schauder fixed point theorem.

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.

Periodic Solutions for Nonlinear Differential Equation with Functional Delay

2008 ◽  
Vol 15 (4) ◽  
pp. 635-642
Author(s):  
Hafsia Deham ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Nonlinear Differential Equation ◽  
Point Theorem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Functional Delay

Abstract We use the modification of Krasnoselskii's fixed point theorem due to T. A. Burton ([Proc. Amer. Math. Soc. 124: 2383–2390, 1996]) to show that the scalar nonlinear differential equation with functional delay 𝑥′(𝑡) = –𝑎(𝑡)𝑥3(𝑡) + 𝐺(𝑡, 𝑥3(𝑡 – 𝑟(𝑡))) has a periodic solution. It is not required that 𝑟(𝑡) be differentiable, while 𝑎 and 𝐺 are continuous with respect to their arguments.

scholarly journals Periodic solutions to a generalized Basener-Ross model with time-dependent coefficients

2022 ◽  
Author(s):  
Zhibo Cheng ◽  
Juan Song
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Green’S Function ◽  
Periodic Solutions ◽  
Green's Function ◽  
Point Theorem ◽  
Continuation Theorem ◽  
Time Dependent ◽  
Mawhin Continuation Theorem

This paper is devoted to studying the existence of at least one periodic solution for a generalized Basener-Ross model with time-dependent coefficients. The discussion is based on the Man\’asevich-Mawhin continuation theorem and fixed point theorem of cone mapping together with some properties of Green’s function.

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 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 Periodic Solutions and Nontrivial Periodic Solutions for a Class of Rayleigh-Type Equation with Two Deviating Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Meiqiang Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Type Equation ◽  
Index Theorem ◽  
Rayleigh Equation ◽  
Deviating Arguments ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions

The Rayleigh equation with two deviating argumentsx′′(t)+f(x'(t))+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=e(t)is studied. By using Leray-Schauder index theorem and Leray-Schauder fixed point theorem, we obtain some new results on the existence of periodic solutions, especially for the existence of nontrivial periodic solutions to this equation. The results are illustrated with two examples, which cannot be handled using the existing results.

scholarly journals Two periodic solutions of neutral difference equations modelling physiological processes

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Neutral Difference Equations ◽  
First Order ◽  
Analysis Techniques ◽  
Physiological Processes

We establish existence, multiplicity, and nonexistence of periodic solutions for a class of first-order neutral difference equations modelling physiological processes and conditions. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.

scholarly journals Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui-Sheng Ding ◽  
Julio G. Dix
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Type System ◽  
Functional Difference ◽  
Difference System ◽  
Multiple Periodic Solutions

This paper is concerned with the existence of multiple periodic solutions for discrete Nicholson’s blowflies type system. By using the Leggett-Williams fixed point theorem, we obtain the existence of three nonnegative periodic solutions for discrete Nicholson’s blowflies type system. In order to show that, we first establish the existence of three nonnegative periodic solutions for then-dimensional functional difference systemyk+1=Akyk+fk, yk-τ, k∈ℤ, whereAkis not assumed to be diagonal as in some earlier results. In addition, a concrete example is also given to illustrate our results.

scholarly journals PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

2010 ◽  
Vol 82 (3) ◽  
pp. 437-445 ◽  
Author(s):  
JIFENG CHU ◽  
ZIHENG ZHANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Schauder’S Fixed Point Theorem ◽  
Positive Periodic Solutions ◽  
Singular Differential Equations ◽  
Attractive Case

AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

scholarly journals Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yuanhong Wei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Function Space ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Second Order Differential Equations

We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.

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