Opuscula Math. 32, no. 1 (2012), 5-19
http://dx.doi.org/10.7494/OpMath.2012.32.1.5
Opuscula Mathematica
Fixed points and stability in neutral nonlinear differential equations with variable delays
Abdelouaheb Ardjouni
Ahcene Djoudi
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.
- Abdelouaheb Ardjouni
- University of Annaba, Department of Mathematics, P.O. Box 12, Annaba 23000, Algeria
- Ahcene Djoudi
- University of Annaba, Department of Mathematics, P.O. Box 12, Annaba 23000, Algeria
- Received: 2011-05-11.
- Accepted: 2011-06-13.
