# ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS BY FIXED POINT THEOREMS

@inproceedings{BurtonASYMPTOTICBO, title={ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS BY FIXED POINT THEOREMS}, author={Theodore A. Burton and Tetsuo Furumochi} }

In a series of papers we have studied stability properties of functional differential equations by means of fixed point theory. We enlarge that study now by also considering delay equations which may be unstable when the delay is zero. We continue to focus on challenging examples to illustrate the work, as opposed to attempting to state general theorems. Here, we deal with three different examples. In Part I we obtain asymptotic stability using Schauder’s and Banach’s fixed point theorems; it…

## 30 Citations

Stability in nonlinear neutral differential equations with infinite delay

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- 2014

Certainly, the Lyapunov direct method has been successfully used to investigate stability properties of a wide variety of ordinary, functional and partial differential equations. Nevertheless, the…

STABILITY BY KRASNOSELSKII'S THEOREM IN TOTALLY NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

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- 2013

In this paper we use fixed point methods to prove asymptotic stability results of the zero solution of a class of totally nonlinear neutral differential equations with functional delay. The study…

Stability in nonlinear neutral differential equations with variable delays using fixed point theory

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- 2011

The purpose of this paper is to use a fixed point approach to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem…

FIXED POINT TECHNIQUES AND STABILITY IN NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS

- Mathematics
- 2013

In this paper we use fixed point techniques to obtain asymptotic stability results of the zero solution of a nonlinear neutral differential equation with variable delays. This investigation uses new…

FIXED POINTS AND STABILITY IN NEUTRAL NONLINEAR DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS

- Mathematics
- 2012

By means of Krasnoselskii's fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and…

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SOME FUNCTIONAL DIFFERENTIAL EQUATIONS BY SCHAUDER’S THEOREM Dedicated to Professor Lásló Hatvani on his 60th birthday

- Mathematics

In a series of papers (Burton-Furumochi [1-4]) we have studied stability properties of functional differential equations by means of fixed point theory. Here we obtain new stability and boundedness…

Fixed points and stability in nonlinear neutral Volterra integro-differential equations with variable delays

- Mathematics
- 2013

Abstract. In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the zero solution of a nonlinear neutral Volterra integro-differential equation with variable…

STABILITY IN TOTALLY NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE DELAY

- Mathematics
- 2014

In this paper, we use a fixed point technique and the concept of large contractions to prove asymptotic stability results of the zero solution of a class of the totally nonlinear neutral differential…

ASYMPTOTIC STABILITY OF DELAY DIFFERENTIAL EQUATIONS VIA FIXED POINT THEORY AND APPLICATIONS

- Mathematics

Nonlinear delay differential equations have been widely used to study the dynamics in biology, but the stability of such equations are challenging. In this paper, new criteria are established for the…

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