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局部凸空间中一类非线性Volterra型积分方程解的存在性 被引量：2

Existence of Solutions to Nonlinear Volterra Integral Equations in Locally Convex Spaces
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摘要 首先利用局部凸空间非紧性测度得到一个新的不动点定理;并运用此定理研究了局部凸空间非线性V o lterra型积分方程解的存在性,然后应用到弱拓扑结构下对非线性V o lterra型积分方程解的存在性的讨论.推广了原有文献的结果. In this paper, first we get a fixed point theroem via the measure of noncompactness in locally convex spaces. Secondly, we apply the above theorem to study the existence of solutions for Volterra integral equations. In particular, we use these results to get the existence of solutions to these equations relative to the weak topology and generalize the results obtained by others.
作者 史红波 朱江
机构地区 淮阴师范学院数学系 徐州师范大学数学系
出处 《应用泛函分析学报》 CSCD 2006年第1期43-50,共8页 Acta Analysis Functionalis Applicata
关键词 局部凸空间 非紧性测度 VOLTERRA型积分方程 不动点 locally convex spaces measure of noncompactness volterra integral equations fixed points
分类号 O177.91 [理学—基础数学] O175.11 [理学—基础数学]
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参考文献9

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共引文献83

同被引文献8

  • 1[2]Toshio Yuasa.Differential equations in a locally convex space via the measure ofnonprecompactness[J].J Math Anal Appl,1981,84:534-554.
  • 2[3]Jacek Polewczak.Ordinary differential equations on closed subsets of locally convex space with applications to fixed point theorems[J].J Math Anal Appl,1990,151:208-225.
  • 3[4]Agase S B.Existence and stability of ordinary differential equations in locally convex spaces[J].Nonlinear Anal,1981,5:713.
  • 4[6]Schaefer H H.Wolff M P.Topological Vector spaces[M].Berlin:Springer,1999.
  • 5[7]Guo Dajun.Extremal solutions of nonlinear Fredholm integral equations in ordered Banach spaces[J].Northeastern Math J,1981,7(4):416-423.
  • 6[8]Heinz H D.On the behavior of measure of non-compactness with respect to differential and integration of vector value functions[J].Nonlinear Anal,1983,7:1351-1371.
  • 7[9]Deimling K.Nonlinear Functional Analysis[M].Berlin:Springer,1988.
  • 8谢胜利,杨志林.Banach空间非线性脉冲Volterra型积分方程和积分-微分方程的可解性[J].数学学报（中文版）,2003,46(3):445-452. 被引量：14

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应用泛函分析学报
2006年 第1期

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