Periodic Solutions For The Second Order Ordinary Differential Equation In Ordered Banach Space

Based on the partial theory,Kuratowski measure of noncompactness,topological degree and fixed point theorem of condensing mapping map,the fixed point index theory in cones,the paper discussed the existence of solutions to the second order periodic boundary value problem of ordinary differential equationin Banach space and the main results are as follow:1.The existence of periodic solutions to the second order ordinary differential equation in Banach space is discussed.On the one hand,by using the monotone iterative method with upper and lower solutions or anti-order upper and lower solutions,the author obtains the existence of maximum solution and minimum solution.On the other hand,only under the condition of order the existence results are obtained,when there are no noncompactness measure condition and the existence of upper and lower solution,which improve and extend the results recently achieved in this field.2.In the case of non-monotone,the existence of the solutions are obtained by employing topological degree and Sadovskii fixed point theorem of condensing mapping,which extend the results recently achieved in this field.3.By employing the fixed point index of condensing mapping,the existence results of positive solution are obtained under two cases,the conclusions extend the results recently achieved in this field.