Opuscula Mathematica
Opuscula Math. 32, no. 1 (), 5-19
Opuscula Mathematica

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

Abstract. 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 sufficient condition is given. The results obtained here extend and improve the work of C. H. Jin and J. W. Luo [Nonlinear Anal. 68 (2008), 3307-3315], and also those of T. A. Burton [Fixed Point Theory 4 (2003), 15-32; Dynam. Systems Appl. 11 (2002), 499-519] and B. Zhang [Nonlinear Anal. 63 (2005), e233-e242]. In the end we provide an example to illustrate our claim.
Keywords: fixed points, stability, nonlinear neutral differential equation, integral equation, variable delays.
Mathematics Subject Classification: 34K20, 34K30, 34K40.
Cite this article as:
Abdelouaheb Ardjouni, Ahcene Djoudi, Fixed points and stability in neutral nonlinear differential equations with variable delays, Opuscula Math. 32, no. 1 (2012), 5-19, http://dx.doi.org/10.7494/OpMath.2012.32.1.5
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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