%0 Journal Article
%T A Remrk on the Existence of Solutions of Initial Value Problem for First order Nonlinear Impulsive Integro-Differential Equation in Banach Space<br>关于Banach空间一阶非线性脉冲积分-微分方程初值问题解存在性的注记
%A XIE Shengli
%A <br>谢胜利
%J 系统科学与数学
%D 2008
%I 
%X Assume that $m(t)\in CJ_k,{\bf R^+}](k=1,2,\cdots,m)$ and $$m(t)\leq (L_1+L_2t)\int_0^tm(s){\rm d}s+L_3t\int_0^am(s){\rm d}s+\sum\limits_{0<t_k<t}M_km(t_k),$$where $L_i\geq0(i=1,2,3),~M_k\geq0 $ satisfy either $$KaL_3\big({\rm e}^{\delta(L_1+aL_2)}-1\big)<L_1+aL_2,$$ or $$a(2L_1+aL_2+aKL_3)<2$$ with $$\delta=\max\limits_{0\leq k\leq m}(t_{k+1}-t_k),\q K=\inf\Big\{d\geq1:\int_0^am(s){\rm d}s\leq d\min\limits_{0\leq k\leq m}\int_{t_k}^{t_{k+1}}m(s){\rm d}s\Big\}.$$Then $m(t)=0,~t\in J$. Firstly, it is shown that the above infimum $K$ is not meaning, and then the existence theorem of solutions of initial value problems is obtained for first order nonlinear impulsive integro-differential equations in Banach spaces under some looser conditions, and hence the existing results are improved.
%K Impulsive integro-differential equation
%K initial value problem
%K measure of noncompactness<br>脉冲积分-微分方程
%K 初值问题
%K 非紧性测度.
%K Banach
%K 空间
%K 一阶非线性
%K 脉冲积分
%K 微分方程
%K 初值问题
%K 解存在性
%K 注记
%K BANACH
%K SPACE
%K EQUATION
%K IMPULSIVE
%K NONLINEAR
%K ORDER
%K INITIAL
%K VALUE
%K PROBLEM
%K 结果
%K 改进
%K 存在性定理
%K 题解
%K 条件
%K 比较
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=D3990B796E19F7658E6FE44E4DD9E0B4&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=E158A972A605785F&sid=BE5DBC360CD4FFB9&eid=F176272DD933A0BB&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=1&reference_num=13