Ahcene Djoudi, Rabah Khemis

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

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

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

MSC 2000: 34K20, 47H10