On oscillation of a Volterra integral equation with delay (Q1085388)

The authors study the equation \[ x(t)=f(t)+\int^{t}_{a}K(t,s,x(s),x(g(s)))ds,\quad t\geq a, \] and give various monotonicity conditions under which the solutions are bounded or unbounded. In addition, solutions that do not tend to zero at infinity are shown to oscillate slowly, i.e., they change sign infinitely often, and the difference between consecutive zeros tends to infinity as \(t\to \infty\).