TY  - JOUR
ID  - Ardjouni2012
LB  - Ardjouni2012
AU  - Ardjouni, Abdelouaheb
AU  - Djoudi, Ahcene
TI  - Fixed points and stability in neutral nonlinear differential equations with variable delays
ST  - Fixed points and stability in neutral nonlinear differential equations with variable delays
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 1
SP  - 5
EP  - 19
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.1.5
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.1.5
AB  - 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.
KW  - fixed points
KW  - stability
KW  - nonlinear neutral differential equation
KW  - integral equation
KW  - variable delays
SN  - 1232-9274
ER  -