Boundedness of solutions of a nonlinear nonautonomous neutral delay equation (Q807829)

The neutral type difference differential equation \[ x'(t)\quad =\quad r(t)x(t) [a(t)-x(t-1)-c(t)x'(t-1)] \] arising in population dynamics is considered. Conditions of boundedness and unboundedness of solutions of the Cauchy problem for this equation formulated in terms of coefficients and initial data are given.