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 PULLBACK ATTRACTORS FOR DIFFERENTIAL EQUATIONS WITH MULTIPLE VARIABLE DELAYS IN LIPSCHITZ NONLINEARITIES

2013 ◽  
Vol 23 (11) ◽  
pp. 1350187 ◽  
Author(s):  
TOMÁS CARABALLO ◽  
GÁBOR KISS ◽  
TAKESHI TANIGUCHI
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Multiple Delays ◽  
Pullback Attractors ◽  
Variable Delays ◽  
Multiple Variable ◽  
Functional Differential

We establish the results on the existence of pullback attractors for nonautonomous functional differential equations with multiple delays appearing within nonlinear Lipschitz terms. The results are complementary to recently presented findings in [Caraballo & Kiss, 2013a, 2013b], and they extend the class of nonlinearities to which existence results can be established by improving on a condition presented in [Caraballo & Kiss, 2013b].

scholarly journals Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Abdellatif Ben Makhlouf ◽  
Lassaad Mchiri ◽  
Mohamed Rhaima
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Systems ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Fixed Point Methods ◽  
Functional Differential ◽  
The Stability ◽  
Rassias Stability ◽  
Stochastic Functional

The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples to show the validity of the results.

scholarly journals Stability and boundedness to certain differential equations of fourth order with multiple delays

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1049-1058 ◽  
Author(s):  
Erdal Korkmaz ◽  
Cemil Tunc
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Multiple Delays ◽  
Boundedness Of Solutions ◽  
Functional Differential ◽  
The Stability

In this paper, we give sufficient conditions to guarantee the asymptotic stability and boundedness of solutions to a kind of fourth-order functional differential equations with multiple delays. By using the Lyapunov-Krasovskii functional approach, we establish two new results on the stability and boundedness of solutions, which include and improve some related results in the literature.

scholarly journals Existence and Exponential Stability of Solutions to Stochastic Neutral Functional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Ling Hu ◽  
Zheng Wu ◽  
Zhangzhi Wei ◽  
Lianglong Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Banach Fixed Point Theorem ◽  
Stability Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Semigroup Approach ◽  
Existence And Stability ◽  
Functional Differential

In this paper we consider the existence and stability of solutions to stochastic neutral functional differential equations with finite delays. Under suitable conditions, the existence and exponential stability of solutions were obtained by using the semigroup approach and Banach fixed point theorem.

scholarly journals Hopf bifurcations in a three-species food chain system with multiple delays

2017 ◽  
Vol 15 (1) ◽  
pp. 508-519 ◽  
Author(s):  
Xiaoliang Xie ◽  
Wen Zhang
Keyword(s):  
Food Chain ◽  
Functional Differential Equations ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Multiple Delays ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Chain System ◽  
Functional Differential ◽  
The Stability

Abstract This paper is concerned with a three-species Lotka-Volterra food chain system with multiple delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the stability of the positive equilibrium and existence of Hopf bifurcations are investigated. Furthermore, the direction of bifurcations and the stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.

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.

Sign in / Sign up

Export Citation Format

Share Document