Boundedness and Asymptotic Behaviour of Solutions of a Second-Order Nonlinear System

Consider the second-order nonlinear system where a is a positive and continuous function onR:(– , ), b, c and h are continuous functions on R, ande is a continuous function on I:0, ). We obtain a sufficientcondition for all solutions of (*) to be bounded, and obtaina sufficient condition for all solutions of (*) to tend to zero.Our results can be applied to the well-known equation which substantially improves and extendsseveral known results in the literature.