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 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 Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Meili Li ◽  
Chunhai Kou
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Existence Results ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Fractional Power Of Operators

The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem.

scholarly journals MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
Xuxin Yang ◽  
Zhimin He ◽  
Jianhua Shen
Keyword(s):  
Differential Equations ◽  
Upper And Lower Solutions ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Second Order ◽  
Monotone Iterative ◽  
Functional Differential ◽  
Extreme Solutions ◽  
Multipoint Boundary Value Problem

This paper is concerned about the existence of extreme solutions of multipoint boundary value problem for a class of second-order impulsive functional differential equations. We introduce a new concept of lower and upper solutions. Then, by using the method of upper and lower solutions introduced and monotone iterative technique, we obtain the existence results of extreme solutions.

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