A Stability Result for the Solutions of a Certain System of Fourth-Order Delay Differential Equation

Abstract

The main purpose of this work is to give sufficient conditions for the uniform stability of the zero solution of a certain fourth-order vector delay differential equation of the following form: $X^{(4)}+F(\dot{X},\ddot{X})\stackrel{⃛}{X}+\mathrm{\Phi }(\ddot{X})+G(\dot{X}(t-r))+H(X(t-r))=0.$ By constructing a Lyapunov functional, we obtained the result of stability.