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分数阶脉冲微分方程边值问题正解的存在性 被引量：6

Existence of Positive Solutions for Boundary Value Problems of Fractional Impulsive Differential Equation
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摘要 用非线性泛函分析理论研究分数阶脉冲微分方程边值问题,借助范数形式的锥拉伸-压缩不动点定理,证明了一类具有Caputo分数导数的脉冲微分方程边值问题正解的存在性,得到了正解存在的充分条件及相应的推论. The boundary value problem of the fractional impulsive differential equation was studied by means of the nonlinear functional theory.Some existence theorems of positive solutions for the boundary value problem of fractional impulsive differential equation with Caputo derivative were proved with the help of the fixed point theorem of cone expansion and compression of norm type, obtaining the sufficient conditions about the existence of positive solutions and the relevant corollary.
作者 智二涛 刘锡平 李凡凡
机构地区 上海理工大学理学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2014年第3期482-488,共7页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:11171220) 上海市教委科研创新重点项目基金(批准号:10ZZ93)
关键词 正解 CAPUTO导数 分数阶脉冲微分方程 不动点定理 positive solutions Caputo derivative fractional impulsive differential equation fixed point theorem
分类号 O175.8 [理学—基础数学]
  • 相关文献

参考文献15

  • 1金京福,刘锡平,窦丽霞,王平友.分数阶微分方程积分边值问题正解的存在性[J].吉林大学学报（理学版）,2011,49(5):823-828. 被引量：16
  • 2LIU Xiping,JIA Mci. Multiple Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions [J]. Comput Math Appl,2010,59(8): 2880-2886.
  • 3JIA Mci,LIU Xiping. Three Nonncgativc Solutions for Fractional Differential Equations with Integral Boundary Conditions [J]. Comput Math Appl,2011,62(3): 1405-14 12.
  • 4FENG Mciqiang,ZHANG Xucmci,GE" Wcigao. New Existence Results for High-Ordcr Nonlinear Fractional Differential Equation with Integral Boundary Conditions [J/OL]. Bound Value Probl,2011,doi: 10. 1 155/201 1/ 720702.
  • 5贾梅,刘锡平.二阶脉冲微分方程积分边值问题多个非负解的存在性[J].吉林大学学报（理学版）,2011,49(4):594-600. 被引量：3
  • 6张学梅,赵向奎,葛渭高.带p-Laplace算子的奇异脉冲微分方程非局部边值问题[J].数学的实践与认识,2009,39(14):213-219. 被引量：2
  • 7BA I Chuanzhi. Existence Rcsuit for Boundary Value Problem of Nonlinear Impulsive Fractional Differential Equation at Resonance [J]. J Appl Math Comput,2012,39( 1/2): 42 1-443.
  • 8CHEN Fulai. Coincidence Degree and Fractional Boundary Value Problems with Impulses [J]. Comput Math Appl,2012,6,1( 10): 3444-3455.
  • 9Ahmad B,WANG Guo-tao.A Study of an Impulsive Four-Point Nonlocal Boundary Value Problem of Nonlinear Fractional Differential Equations [J]. Comput Math Appl,2011,62(3): 134 1-134 9.
  • 10TIAN Yuanshcng,BAI Zhanbing. Existence Results for the Thrcc-Point Impulsive Boundary Value Problem Involving Fractional Differential Equations [J]. Comput Math Appl,2010,59(8): 2601-2609.

二级参考文献31

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  • 10LIU Xi-ping, JIA Mei. Multiple Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions [ J]. Computers and Mathematics with Applications, 2010, 59 : 2880-2886.

共引文献17

同被引文献19

引证文献6

二级引证文献9

吉林大学学报（理学版）
2014年 第3期

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