Banach空间中二阶非线性脉冲微分-积分方程的初值问题

Initial Value Problems for Nonlinear Second Order Impulsive Integro-differential Equations in Banach Space

通过引进等价的范数，应用Ｂａｎａｃｈ不动点定理，在较宽松的条件下，获得了Ｂａｎａｃｈ空间中 二阶非线性脉冲微分－积分方程初值问题解的存在与唯一性及解的迭代逼近．对文［５］（Ｊ．Ｍａｔｈ． Ａｎａｌ．Ａｐｐｌ．２００（１９９６），１—１３）相应于ｄ０＝０的结果作了重要改进和推广．该文条件易于判断，方 法也本质地不同于文［５］．

Through intrducing the equivalent norm,by applying Banach fixed theorem,un- der simpler conditions,the author has obtained existence and uniqueness and iterative approximation of solution for initial value problems of nonlinear second order impulsive integro-differential equations in Banach space,and improved and generalized the corresponding results of paper [5] for d0=0 (J. Math. Anal. Appl. 200(1996), 1 - 13). The assumed condition in present paper is easy to be judged and the method is different essentially from the one in paper [5].