# Stability in Nonlinear Delay Volterra Integro-differential Systems

Volume 7, Issue 6, pp 422--428
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### Authors

Youssef Raffoul - Department of Mathematics, University of Dayton, Dayton, OH 45469-2316, USA. Mehmet Ünal - Faculty of Education, Sinop University, 5700 Sinop, Tutkey.

### Abstract

We employ Lyapunov functionals to the system of Volterra integro-differential equations of the form $x'(t) = Px(t) - \int^ t _{t-r} C(t; s)g(x(s))ds,$ and obtain conditions for the stability of the of the zero solution. In addition, we will furnish an example as an application.

### Keywords

• Volterra integro-differential equations
• zero solution
• stability
• Lyapunov functional

•  3K20
•  45J05

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