The Solutions Of Periodic Boundary Value Problems Of First Order Impulsive Differential Equations In Banach Spaces

In this paper, by using the monotone iterative techinque in presence of upper and lower solutions firstly, we discuss the existence of solutions for periodical boundary value problems of first-order impulsive differential equationsin Banach space E, where f∈C(J×E,E), J=[0,ω], Ik∈C(E,E), k1,2,…,m.Secondly, by using the fixed point theorem of condensing mapping and the fixed point index theory in cones respectively, we discuss the existence of solutions for periodical boundary value problems of first-order impulsive differential equations the existence of positive solutions in Banach space, where f, Ik(k=1,2,…,m) are defined as above.The results of this paper are as follows:1. Combining with the monotone iterative techinque in presence of upper and lower solutions, we obtain the existence of the minimal and maximal solutions and the uniqueness of solution for periodical boundary value problems of first-order impulsive differential equations in order Banach spaces. 2. Under the conditions of measure of noncompactness, by using the fixed point theorem of condensing mapping, we obtain the existence of solutions for periodical boundary value problems of first-order impulsive differential equations.3. Under the conditions of measure of noncompactness, by using the fixed point index theory in cones, we obtain the existence of positive solutions for periodical boundary value problems of first-order impulsive differential equations.