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

• Main Authors: Abdelouaheb Ardjouni, Ahcene Djoudi
• Format: Article
• Language: English
• Published: University of Szeged 2013-05-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: fixed points; stability; neutral volterra integro-differential equation; variable delays
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=2160

In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the zero solution of a nonlinear neutral Volterra integro-differential equation with variable delays. Some conditions which allow the coefficient functions to change sign and do not ask the boundedness of delays are given. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improve and extend the results in the literature. Two examples are also given to illustrate this work.