Asymptotic behaviour of a two-dimensional differential system with delay under the conditions of instability (Q2486618)

The real two-dimensional system \[ x'(t) = A(t)x(t) + B(t)x(t - r) + h(t, x(t), x(t - r)),\quad t \geq t_0, \] is considered, where \(A(t)\) and \(B(t) \) are real matrices and \(h(t,x,y)\) is a vector function. Sufficient conditions for the existence of bounded solutions or solutions tending to the zero as \(t\) tends to \(+\infty\) are given.