Stability in nonlinear neutral differential equations with variable delays using fixed point theory

Abstract

The purpose of this paper is to use a fixed point approach to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved. In our consideration we allow the coefficient functions to change sign and do not require bounded delays. The obtained results improve and generalize those due to Burton, Zhang and Raffoul. We end by giving three examples to illustrate our work.

Keywords

• fixed points
• stability
• neutral differential equation
• integral equation
• variable delays