期刊信息

  • 刊名: 河北师范大学学报(自然科学版)Journal of Hebei Normal University (Natural Science)
  • 主办: 河北师范大学
  • ISSN: 1000-5854
  • CN: 13-1061/N
  • 中国科技核心期刊
  • 中国期刊方阵入选期刊
  • 中国高校优秀科技期刊
  • 华北优秀期刊
  • 河北省优秀科技期刊

二阶非线性积分-微分方程边值问题的正解

  • 西北师范大学 数学与统计学院, 甘肃 兰州 730070
  • DOI: 10.11826/j.issn.1000-5854.2014.05.003

Positive Solutions of Nonlinear Second-order Boundary Value Problems for Integro-differential Equations

摘要/Abstract

摘要:

用锥映射不动点定理讨论了一类新的非线性二阶积分-微分方程边值问题正解的存在性,所研究的问题更具一般性,推广了已有的一些结果。

Abstract:

In this paper,the existence of positive solutions of boundary value problem for a new class of nonlinear second-order integro-differential equations is discussed by employing the fixed point theorem of cones map.The research question is much more general and extended a number of existing work.

参考文献 16

  • [1] CABADA A.The Method of Lower and Upper Solution for Second,Third,Fourth and High Order Boundary Value Problems [J].J Math Anal Appl,1994,185:302-320.
  • [2] ZHUANG W,CHEN Y B.PBVP of Integro-differential Equations with Caratheodory Functions [J].Acta Mathematica Sinica,1998,14(4):463-472.
  • [3] 宋光兴.Banach空间积-微分两点边值问题 [J].数学学报,2000,43(3):555-560.
  • [4] 孙经先,刘立山.Banach空间中混合型微分-积分方程的单调迭代方法 [J].系统科学与数学,1993,13(2):160-166.
  • [5] 刘立山.Banach空间非线性混合型微分-积分方程的解 [J].数学学报,1995,38(6):721-731.
  • [6] 宋光兴.Banach空间中二阶积-微分方程初值问题的解 [J].数学学报,2004,47(1):71-78.
  • [7] HE Z,HE X.Monotone Iterative Technique for Impulsive Integro-differential Equations with Periodic Boundary Conditions [J].Comput Math Appl,2004,48:73-84.
  • [8] 王文霞.一类二阶非线性积分-微分方程的边值问题 [J].工程数学学报,2005,22(3):555-558.
  • [9] 张晓燕,孙经先,苏军.Banach空间中二阶非线性微分积分方程周期边值问题 [J].工程数学学报.2004,21(6):1041-1044.
  • [10] 周友明.Banach空间中二阶微分方程的周期边值问题 [J].应用数学学报,2006(4),436-444.
  • [11] 谢胜利.Banach空间二阶非线性脉冲积分-微分方程初值问题 [J].数学物理学报,2007(1),138-145.
  • [12] SU H,LIU L S,ZHANG X Y,et al.Global Solution of Initial Value Problems for Nonlinear Second-order Integro-differential Equations of Mixed Type in Banach Space [J].J Math Anal Appl,2007,330:1139-1151.
  • [13] NIETO J J,RODRIGUEZ R L.New Comparison Results for Impulsive Integro-differential Equations and Applications [J].J Math Anal Appl,2007,328:1343-1368.
  • [14] 李永祥,晏锐.二阶非线性积分-微分方程边值问题的正解 [J].兰州大学学报:自然科学版,2002,38(4):1-6.
  • [15] MA D,TIAN Y,GE W.Existence Theorems of Positive Solutions for a Fourth-order Three-point Boundary Value Problem [J].Taiwanese J Math,2006,10(6):1557-1573.
  • [16] 郭大钧.非线性泛函分析 [M].济南:山东科学技术出版社,1985:286-328.