On The Existence Of Periodic Solutions For The Differential Equation And Some Applications On The Biology

The existence of solutions of Differential Equation is one of basical problems of Differential Equation .In many years,some scholars have studied it extensively and deeply. As is known to all,there are some phenomena and problems in nature and society. So studying the existence of solutions of Differential Equation ,not only has important significance,but real value.In this paper,by using the continuation theorem of Mawhin'coincidence degree theory,we study the existence of periodic solutions for a kind of second order Differential Equation with a deviating argument and continuation delay,suffcient criteria are established for the existence of periodic solutions.Similarly,as for concret applications of Differential Equation on the biology,we study the existence of positive periodic solutions and global existence of solutions for a kind of n-species Lotka-Volterra competitive model and a predator-prey system with Holling II type functional response,some sufficient criteria are obtained.