scholarly journals Fixed Point Theorems and Uniqueness of the Periodic Solution for the Hematopoiesis Models

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Continuous Function ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Equivalent Norm ◽  
Multiple Delays ◽  
Functional Differential ◽  
Continuous Function Space

We present some results to the existence and uniqueness of the periodic solutions for the hematopoiesis models which are described by the functional differential equations with multiple delays. Our methods are based on the equivalent norm techniques and a new fixed point theorem in the continuous function space.

scholarly journals Smooth Solutions of a Class of Iterative Functional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Houyu Zhao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Smooth Solutions ◽  
Functional Differential ◽  
Iterative Functional Differential Equation

By Faà di Bruno’s formula, using the fixed-point theorems of Schauder and Banach, we study the existence and uniqueness of smooth solutions of an iterative functional differential equationx′(t)=1/(c0x[0](t)+c1x[1](t)+⋯+cmx[m](t)).

scholarly journals J-nonexpansive mappings in uniform spaces and applications

1991 ◽  
Vol 43 (2) ◽  
pp. 331-339 ◽  
Author(s):  
Vasil G. Angelov
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Functional Differential Equations ◽  
Uniform Convexity ◽  
Existence Theory ◽  
Uniform Spaces ◽  
Geometric Properties ◽  
Functional Differential

The purpose of the paper is to introduce a class of “j-nonexpansive” mappings and to prove fixed point theorems for such mappings. They naturally arise in the existence theory of functional differential equations. These mappings act in spaces without specific geometric properties as, for instance, uniform convexity. Critical examples are given.

scholarly journals Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Yunhui Zeng
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Positive Periodic Solution ◽  
Multiple Delays ◽  
Neutral Delay ◽  
Mawhin’S Continuation Theorem ◽  
Volterra Models ◽  
Functional Differential ◽  
New Criteria

By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory fork-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse:x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))],  t≠tk,  k∈Z+;  x(tk+)=x(tk-)+θk(x(tk)),  k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.

scholarly journals Existence Results for Semilinear Functional Differential System with Nonlocal Conditions

2018 ◽  
Vol 8 (10S) ◽  
pp. 237-241
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Abstract Space ◽  
Functional Differential ◽  
Functional Differential System

In this paper, sufficient conditions are given for the existence of partial functional differential equations with nonlocal conditions in an abstract space with the help of the fixed point theorems.

scholarly journals Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Lokesh Budhia ◽  
Hassen Aydi ◽  
Arslan Hojat Ansari ◽  
Dhananjay Gopal
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Existence Of A Solution ◽  
Rectangular Metric Space ◽  
Functional Differential

In this paper, we establish some new fixed point theorems for generalized ϕ–ψ-contractive mappings satisfying an admissibility-type condition in a Hausdorff rectangular metric space with the help of C-functions. In this process, we rectify the proof of Theorem 3.2 due to Budhia et al. [New fixed point results in rectangular metric space and application to fractional calculus, Tbil. Math. J., 10(1):91–104, 2017]. Some examples are given to illustrate the theorems. Finally, we apply our result (Corollary 3.6) to establish the existence of a solution for an initial value problem of a fractional-order functional differential equation with infinite delay. 

scholarly journals On Random Periodic Solution to a Neutral Stochastic Functional Differential Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lili Gao ◽  
Litan Yan
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Brownian Motion ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Stochastic Functional Differential Equation ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we consider the random periodic solution to a neutral stochastic functional differential equation driven by Brownian motion. We obtain the existence and uniqueness of the random periodic solution by Banach fixed point theorem. Moreover, we introduce two examples to illustrate our results.

Existence results for systems of coupled impulsive neutral functional differential equations driven by a fractional Brownian motion and a Wiener process

2019 ◽  
Vol 27 (4) ◽  
pp. 225-242
Author(s):  
Tayeb Blouhi ◽  
Mohamed Ferhat
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Wiener Process ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Neutral Functional Differential Equations ◽  
Fractional Brownian Motions ◽  
Functional Differential

Abstract In this paper, we prove some results on the existence and uniqueness of mild solutions for a system of semilinear impulsive differentials with infinite fractional Brownian motions and a Wiener process. Our approach is based on a new version of fixed point theorem, due to Krasnoselskii, in generalized Banach spaces.

scholarly journals Stability to a Kind of Functional Differential Equations of Second Order with Multiple Delays by Fixed Points

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Cemil Tunç ◽  
Emel Biçer
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Differential Equations ◽  
Multiple Delays ◽  
Stability Of Solutions ◽  
Variable Delays ◽  
Multiple Variable ◽  
Fixed Point Technique ◽  
Functional Differential ◽  
The Stability

We discuss the stability of solutions to a kind of scalar Liénard type equations with multiple variable delays by means of the fixed point technique under an exponentially weighted metric. By this work, we improve some related results from one delay to multiple variable delays.

scholarly journals Periodic solutions for some partial functional differential equations

2004 ◽  
Vol 2004 (1) ◽  
pp. 9-18 ◽  
Author(s):  
Rachid Benkhalti ◽  
Khalil Ezzinbi
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Bounded Solution ◽  
Linear Part ◽  
Functional Differential Equations ◽  
Nonlinear Case ◽  
Partial Functional Differential Equations ◽  
Functional Differential

We study the existence of a periodic solution for some partial functional differential equations. We assume that the linear part is nondensely defined and satisfies the Hille-Yosida condition. In the nonhomogeneous linear case, we prove the existence of a periodic solution under the existence of a bounded solution. In the nonlinear case, using a fixed-point theorem concerning set-valued maps, we establish the existence of a periodic solution.

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