NECESSARY AND SUFFICIENT CONDITIONS FOR THE OSCILLATIONS OF A MULTIPLICATIVE DELAY LOGISTIC EQUATION

Necessary and sufficient conditions are presented for the oscillation of all positive solutions of the multiplicative delay logistic equation [GRAPHICS] about the positive equilibrium K. The cases when r(t) = r and g(j)(t) = t - tau(j) or g(j)(t) = [t - k(j)], [.] denoting the greatest integer function, where r, tau(j), and k(j) are positive constants, j = 1, 2,..., m, are also included.