Qualitative Research Of Neutral Functional Differential Equations

This paper consists of four chapters, which mainly studies the existence of nonoscillatory solutions and periodic solutions of several kinds of Neutral Functional differential equations. A series of new results are obtained, and some of them improve or extend the related results in the literatures.Chapter 1 introduces the background of the problem-researching in this field. Chapter 2 considers the existence of nonoscillatory solutions of the equationd~2/dt~2[y(t) - P(t)y(t - t)] + q(t)f(y(t - a)) = 0,and some sufficient conditions are established.Chapter 3 concerns the existence of a unique periodic solution of the equation[y{t) -p(t)y(t - r)]" + f(t,y(t),y(t - r)) = 0,and extended some relatated results .Chapter 4 considers the existence of positive solutions of equationsand[a(t)[y(t) - p(t)y(t - T)]']" - f(t, y(g(t)) = 0,and some new results are obtained by using the Fixed Point Theorem.