OSCILLATIONS AND CONVERGENCE IN A DIFFUSIVE DELAY LOGISTIC EQUATION

Sufficient conditions are obtained for all positive solutions of the d iffusive delay-logistic system partial derivative N(x, t)/partial deri vative t = D partial derivative 2N(x, t)/partial derivative x2 + rN(x, t)[1- N(x, t - tau/K] partial derivative N/partial derivative x(x, t) = 0 for x = 0, x = l and t greater-than-or-equal-to - tau to be oscil latory about the positive equilibrium K. A comparison result is establ ished with which the global asymptotic stability of the positive equil ibrium is investigated.