Stability properties of the solutions of the nonlinear functional differential systems (Q1323190)

The asymptotic behaviour of the solutions (boundedness in particular) of the functional differential equation \(y'(t)= f(t,y(t))+ g(t,y(t),Ty(t))\) are studied on the basis of the corresponding behaviour of the equation \(x'(t)= f(t,x(t))\), where \(y(t)\), \(x(t)\in \mathbb{R}^ n\) and \(T\) is a functional. The authors use the technique of nonlinear integral inequalities to find conditions for asymptotic equivalence between both systems.