Stability results for nonlinear functional differential equations using fixed point methods

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 coef...

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Bibliographic Details
Published in:Indagationes mathematicae 2018-04, Vol.29 (2), p.671-686
Main Authors: Chen, Guiling, Li, Dingshi, van Gaans, Onno, Verduyn Lunel, Sjoerd
Format: Article
Language:English
Subjects:
(neutral) integro-differential equation
Asymptotic stability
Contraction mapping principle
Differential equations
Fixed point theory
Fixed points (mathematics)
Mathematical analysis
Mathematics
Nonlinear equations
Stability
Variable delay
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Summary: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.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2017.11.004