Banach空间一阶脉冲积分-微分方程初值问题解的存在性The existence of solution of intial value problem for the first order impulsive integro-differential equations in Banach spaces
姜燕君;刘立山;
摘要(Abstract):
利用M o。nch不动点定理和比较结果,研究了实Banach空间中一阶非线性脉冲微分-积分方程的初值问题解的存在性,本文对已有结果作了推广和改进.
关键词(KeyWords): 脉冲方程;初值问题;不动点;非紧性测度
基金项目(Foundation): 国家自然科学基金资助项目(10471075);; 山东省自然科学基金资助项目(Y2003A01,02BS119)
作者(Authors): 姜燕君;刘立山;
参考文献(References):
- [1]L akshm ikan tham V,L ee la S.O n the m ethod of upper and low er so lu tions in abstract cone[J].A nn.Po lon M ath.,1983,ⅩⅢ:159-164.
- [2]Zang Z Q.A note on the theorem of L akshm ikan tham and L ee la[J].A pp l.M ath.Com pu t.,1986,23(3):269-275.
- [3]L akshm ikan tham V,L ee la s,V atsa la A S.M ethod of quas i-upper and low er so lu tions in abstract cone[J].N on linear.A na l.,1982,6(8):833-838.
- [4]H ao Zhaoca i,L iu L ishan.G loba l so lu tions of in itia l va lue prob lem s for non linear in tegra l-d ifferen tia lequations of m ixed type in B anach spaces[J].Ind ian J.pure app l.M ath.,2002,33(9):1417-1430.
- [5]H e inz H D.O n the behav iour of m easures of noncom pactness w ith respect to d ifferen tiation andin tegration of vector-va lued functions[J].N on linear A na l.,1983,7:416-423.
- [6]刘立山.B anach空间非线性混合型微分-积分方程初值问题整体解的存在性[J].系统科学与数学,2000,20(1):112-116.
- [7]D e im ling K.N on linear Functiona l A na lys is[M].B erlin:Spring-verlag,1985.
- [8]刘立山.B anach空间非线性混合型微分-积分方程的解[J].数学学报,1995,38(2):721-731.
- [9]Lu Hu iq in.Ex terna l so lu tions of non linear first order im pu ls ive in tgro-d ifferen tia l equa itons in B anachspace[J].Ind ian J.Pure A pp l.M ath.,1999,30(11):1181-1197.
- [10]G uo D a jun,L akshm ikan tham V,L iu X inzh i.N on linear In tegra l Equations in A bstract Spaces[M].D ordrech t:K luw er A cdem ic Pub lishers,1996.
- [11]L iu L ishan,Zhang X iaoyan,K im Jong K yu.Ex istence of g loba l so lu tions of in tia l va lue prob lem fornon linear im pu ls ive in tegro-d ifferen tia l equations of m ixed type in B anach spaces[J].N on linear Funct.A na l.A pp l.,2001,6(3):313-327.
- [12]于立新,刘立山.B anach空间中一阶非线性脉冲积分-微分方程初值问题解的存在性[J].系统科学与数学,2003,23(2):257-265.