**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