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

Ardjouni A., Djoudi A.

Opuscula Mathematica

2012

Vol. 32, no. 1

5-19

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.

Oscillatory behaviour of the second-order nonlinear neutral defferential equations with distributed delay

Jundong B., Yongzhen H.

Demonstratio Mathematica

1999

Vol. 32, nr 1

21-30

In this paper, the oscillatory behaviour of second-order nonlinear neutral differential equations with distributed delay was examined, some exciting results were obtained which developed some traditional results in history.