Ahcene Djoudi, Rabah Khemis

Fixed Point Techniques and Stability for Neutral Nonlinear Differential Equations with Unbounded Delays

Abstract:
We use the contraction mapping theorem to obtain stability results of the scalar nonlinear neutral differential equation with functional delay
$$ x^{\prime }(t)=-ax(t)+b(t)x^{2}(t-r(t))+c(t)x(t-r(t))x^{\prime }(t-r(t)).$$

Keywords:
Contraction mapping, stability, nonlinear neutral differential equation, integral equation.

MSC 2000: 34K20, 47H10