Periodic Solution And Periodic Boundary Value Problem Of Differential Equations

The paper discuss periodic boundary value problem for first order impulsive differential equation, the existence of periodic solution for neutral functional differential equation and extremal solution for seconder order functional differential equations with periodic boundary value condition.Using the fixed point theorem in a cone, we obtained the existence and multiplicity of positive solutions, which we are different with that of in the literature.By applying to schauder ’s fixed point theorem,we study the existence of periodic solution for neutral functional differential equation with infinite distributed delay and our results only need that the nonlinear terms satisfy the given conditions on some closed set, we obtain the existence of extreme solution for second order functional different equation with periodic boundary value condition by using monotone method under existing upper and lower solutions in the reverse order.