## Stability and boundedness of solutions of a certain $$n$$-dimensional nonlinear delay differential system of third-order.(English)Zbl 1352.34099

Summary: By defining suitable Lyapunov functionals, we investigate proper sufficient conditions for the uniform stability of the zero solution, and also for the uniform boundedness and uniform ultimate boundedness of all solutions of a certain third-order nonlinear vector delay differential equation of the type $\dddot {X} + A\ddot {X} + G(\dot{X}) + H(X(t-r)) = P(t).$

### MSC:

 34K20 Stability theory of functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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