Stability results for nonlinear functional differential equations using fixed point methods

Guiling Chen; Dingshi Li; Onno van Gaans; Sjoerd Verduyn Lunel

doi:10.1016/j.indag.2017.11.004

Stability results for nonlinear functional differential equations using fixed point methods

Guiling Chen, Dingshi Li^*, Onno van Gaans, Sjoerd Verduyn Lunel

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We present new conditions for stability of the zero solution for three distinct classes of scalar nonlinear delay differential equations. Our approach is based on fixed point methods and has the advantage that our conditions neither require boundedness of delays nor fixed sign conditions on the coefficient functions. Our work extends and improves a number of recent stability results for nonlinear functional differential equations in a unified framework. A number of examples are given to illustrate our main results.

Original language	English
Pages (from-to)	671-686
Number of pages	16
Journal	Indagationes Mathematicae
Volume	29
Issue number	2
DOIs	https://doi.org/10.1016/j.indag.2017.11.004
Publication status	Published - 1 Apr 2018

Keywords

(neutral) integro-differential equation
Asymptotic stability
Contraction mapping principle
Fixed point theory
Variable delay

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10.1016/j.indag.2017.11.004

1-s2.0-S0019357717301349-mainFinal published version, 270 KBLicence: Taverne

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abstract = "We present new conditions for stability of the zero solution for three distinct classes of scalar nonlinear delay differential equations. Our approach is based on fixed point methods and has the advantage that our conditions neither require boundedness of delays nor fixed sign conditions on the coefficient functions. Our work extends and improves a number of recent stability results for nonlinear functional differential equations in a unified framework. A number of examples are given to illustrate our main results.",

keywords = "(neutral) integro-differential equation, Asymptotic stability, Contraction mapping principle, Fixed point theory, Variable delay",

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AU - Chen, Guiling

AU - Li, Dingshi

AU - van Gaans, Onno

AU - Verduyn Lunel, Sjoerd

PY - 2018/4/1

Y1 - 2018/4/1

N2 - We present new conditions for stability of the zero solution for three distinct classes of scalar nonlinear delay differential equations. Our approach is based on fixed point methods and has the advantage that our conditions neither require boundedness of delays nor fixed sign conditions on the coefficient functions. Our work extends and improves a number of recent stability results for nonlinear functional differential equations in a unified framework. A number of examples are given to illustrate our main results.

AB - We present new conditions for stability of the zero solution for three distinct classes of scalar nonlinear delay differential equations. Our approach is based on fixed point methods and has the advantage that our conditions neither require boundedness of delays nor fixed sign conditions on the coefficient functions. Our work extends and improves a number of recent stability results for nonlinear functional differential equations in a unified framework. A number of examples are given to illustrate our main results.

KW - (neutral) integro-differential equation

KW - Asymptotic stability

KW - Contraction mapping principle

KW - Fixed point theory

KW - Variable delay

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JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 2

ER -

Stability results for nonlinear functional differential equations using fixed point methods

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