Oscillation and at tractivity in a differential equation with piecewise constant arguments

Let [•] denote the greatest integer function. Consider the equation with piecewise constant arguments (formula precented) where r is a positive number and for j ∈ {0, 1,…, m}, kj is a nonnegative integer and aj and bj are nonnegative real numbers. We obtain necessary and sufficient conditions for all positive solutions of (*) to oscillate about its positive equilibrium, we provide sufficient conditions for the positive equilibrium of (*) to be a global attractor of all positive solutions, and we establish that every positive solution of (*) is bounded from above and from below by positive constants. © 1993 Rocky Mountain Mathematics Consortium.