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脉冲型算子微分包含解的存在性 被引量：1

Existence of mild solutions to impulsive differential inclusions
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摘要 利用Hausdorff非紧测度、迭代和多值分析的方法,研究Banach空间中非局部脉冲微分包含适度解的存在性,去除了这类问题中对算子半群紧性的约束条件,改进了已有的相关结果. By using Hausdorff＇s measure of noncompactness, iterative method and multivalued analysis, this author discusses the existence of mild solutions to nonlocal impulsive differential inclusions in Banach spaces. The restriction on the compactness of operator semigroup is removed, which improves some related results in this area.
作者 嵇绍春 李刚
机构地区 淮阴工学院数理学院 扬州大学数学科学学院
出处 《扬州大学学报（自然科学版）》 CAS 北大核心 2015年第4期24-27,67,共5页 Journal of Yangzhou University：Natural Science Edition
基金 国家自然科学基金资助项目(11271316) 江苏省自然科学基金资助项目(BK20150415) 江苏省高校自然科学研究面上资助项目(14KJB110001)
关键词 脉冲微分包含 非局部条件 非紧测度 多值分析 impulsive differential inclusions nonlocal conditions measure of noncompactness multivalued analysis
分类号 O175.15 [理学—基础数学]
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参考文献11

  • 1BENCHOHRA M, HENDERSON J, NTOUYAS S. Impulsive differential equations and inclusions [M]. New York: Hindawi Publishing Corporation, 2006:1 62.
  • 2EAN Zhenbin, LI Gang. Existence results for semilinear differential equations with nonlocal and impulsive condi- tions [J]. J Funct Anal, 2010, 258(5): 1709 1727.
  • 3嵇绍春,李刚.脉冲条件下半线性微分包含的适度解[J].黑龙江大学自然科学学报,2013,30(4):483-487. 被引量：1
  • 4BYSZEWSKI L. Theorems about the existence and uniqueness of solutions o{ a semilinear evolution nonlocal Cauchy problem [J]. J Math Anal Appl, 1991,162(2): 494 505.
  • 5练婷婷,李刚.非局部条件下积分微分方程适度解的存在性[J].扬州大学学报（自然科学版）,2014,17(2):16-19. 被引量：1
  • 6JI Shaochun. Approximate controllability of semilinear nonlocal fractional differential systems via an approxima- ting method [J]. Appl Math Comput, 2014, 236: 43-53.
  • 7BANA J, GOEBEL K. Measures of noncompactness in Banach spaces [M]//Lecture Notes in Pure and Applied Math. New York.. Marcel Dekker, 1980.. 6-65.
  • 8嵇绍春,李刚.非局部条件下脉冲微分方程的适度解[J].扬州大学学报（自然科学版）,2010,13(1):13-16. 被引量：5
  • 9CARDINALI T, RUBBIONI P. On the existence of mild solutions of semilinear evolution differential inclusions [J]. J Math Anal Appl, 2005, 308(2): 620-635.
  • 10ZHU Lanping, LI Gang. On a nonlocal problem for semilinear dif{erential equations with upper semicontinuous nonlinearities in general Banach spaces [J]. J Math Anal Appl, 2008, 341(1); 660 675.

二级参考文献32

  • 1LIANG Jin, LIU James H, XIAO Ti j un. Nonlocal impulsive problems for nonlinear differential equations in Banach spaces [J]. Math Comput Model, 2009, 49(3/4): 798-804.
  • 2BENCHOHRA M, HENDERSON J, NTOUYAS S K, et al. On first order impulsive dynamic equations on time scales [J]. J Difference Equ Appl, 2004, 10(6):541-548.
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  • 4BYSZEWSKI L. Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem [J]. J Math Anal Appl, 1991,162(2):494-505.
  • 5LIANG Jin, LIU James H, XIAO Ti-jun. Nonlocal Cauehy problems governed by compact operator families [J]. Nonlinear Anal, 2004, 57(2): 183-189.
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  • 7CARDINALI T, RUBBIONI P. On the existence of mild solutions of semilinear evolution differential inclusions [J]. J Math Anal Appl, 2005, 308(2): 620-635.
  • 8BANAS J, GOEBEL K. Measure of noncompactness in Banach spaces [M]//BANAS J. Lecture Notes in Pure & Applied Math. New York: Dekker, 1980: 9-60.
  • 9HEINZ H P. On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions [J]. Nonlinear Anal TMA, 1983, 7(12): 1351-1371.
  • 10MONCH H. Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces [J]. Nonlinear Anal: Theory, Melhods &. Appl, 1980, 4(5) : 985-999.

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扬州大学学报（自然科学版）
2015年 第4期

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