In this paper, we study the asymptotic stability of a generalized nonlinear neutral differential equation with variable delays by using the fixed point theory. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton b5, Zhang z, Dib, Maroun and Raffoul d1, and Ardjouni and Djoudi a2.1. An example is also given to illustrate our results

Ardjouni, Abdelouaheb

Djoudi, Ahcene

University of Niš: Facta Universitatis (E-Journals) / Универзитет у Нишу

ASYMPTOTIC STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS

Abstract. In this paper, we study the asymptotic stability of a generalized nonlinear neutral differential equation with variable delays by using the fixed point theory. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton [11], Zhang [25], Dib, Maroun and Raffoul [16], and Ardjouni and Djoudi [3]. Two examples are also given to illustrate our results

Abdelouaheb Ardjouni

Ahcene Djoudi

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