Sharp conditions for the oscillation of delay difference equations

Suppose that {pn} is a nonnegative sequence of real numbers and let k be a positive integer. We prove that limn→∞inf [1k∑i=n−kn−1pi]>kk(k+1)k+1 is a sufficient condition for the oscillation of all solutions of the delay difference equation An+1−An+pnAn−k=0,   n=0,1,2,…. This result is sharp in that the lower bound kk/(k+1)k+1 in the condition cannot be improved. Some results on difference inequalities and the existence of positive solutions are also presented

Global attractivity in population dynamics

We established sufficient conditions for the global attractivity of the positive equilibrium of the delay differential equation N(t)=-mu;N(t)+ ∑ i=1 m pi exp[-γN(t-τi)], t≥0, m≥1. For m = 1, equation (1) was used by Wazewska-Czyzewska and Lasota as a model for the survival of red-blood cells in an animal. © 1989

Comparison results for oscillations of delay equations

We established a comparison result for the oscillation of all solutions of the linear delay equation with positive and negative coefficients {Mathematical expression} in terms of the oscillation of the « limiting » equation {Mathematical expression} where p= lim inf P(t) and q=lim sup Q(t). t→∞ t→∞ Next, we employed the above result to obtain comparison results for the oscillation of all solutions (or all bounded solutions) of a nonlinear delay equation {Mathematical expression} in terms of the oscillation of the linearized equation. © 1990 Fondazione Annali di Matematica Pura ed Applicata

On a nonlocal Cauchy problem for differential inclusions

We establish sufficient conditions for the existence of solutions for semilinear differential inclusions, with nonlocal conditions. We rely on a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler andon the Schaefer's fixed-point theorem combined with lower semicontinuous multivalued operators with decomposable values