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脉冲条件下半线性微分包含的适度解 被引量：1

Mild solutions to impulsive semilinear differential inclusions
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摘要 在广义的Banach空间中研究带有脉冲条件的非局部半线性微分包含,给出非局部项Lipschitz条件下脉冲微分系统适度解存在的充分条件。在相应算子半群等度连续的条件下,利用多值映射不动点定理和非紧测度的方法,对脉冲函数项和扰动项的紧性条件与Lipschitz条件进行统一处理。给出一个例子说明抽象结果。 The mild solutions to impulsive nonlocal differential inclusions in general Banach spaces are considered. The sufficient conditions for the mild solutions to the impulsive differential system are given when the nonlocal item is Lipschitz continuous. By using muhivalued fixed point theorem and measure of noncompactness, the compacness and Lipschitz continuity of impulsive functions are dealt with in a unified way when the associated operator semig- roup is equicontinuous. An example is given to illustrate the obtained abstract result.
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 《黑龙江大学自然科学学报》 CAS 北大核心 2013年第4期483-487,共5页 Journal of Natural Science of Heilongjiang University
基金 国家自然科学基金资助项目(11271316) 江苏省高校自然科学研究项目(11KJB110018) 淮阴工学院青年基金资助项目(HGC1229)
关键词 脉冲微分包含 非局部条件 非紧测度 不动点 impulsive differential inclusions nonlocal conditions measure of noncompactness fixed point
分类号 O175.15 [理学—基础数学]
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参考文献11

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二级参考文献19

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共引文献4

同被引文献10

  • 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.
  • 3BYSZEWSKI 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.
  • 4JI Shaochun. Approximate controllability of semilinear nonlocal fractional differential systems via an approxima- ting method [J]. Appl Math Comput, 2014, 236: 43-53.
  • 5BANA J, GOEBEL K. Measures of noncompactness in Banach spaces [M]//Lecture Notes in Pure and Applied Math. New York.. Marcel Dekker, 1980.. 6-65.
  • 6CARDINALI T, RUBBIONI P. On the existence of mild solutions of semilinear evolution differential inclusions [J]. J Math Anal Appl, 2005, 308(2): 620-635.
  • 7ZHU 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.
  • 8BOTHE D. Multivalued perturbations of m-accretive differential inclusions [J]. Israel J Math, 1998, 108(1): 109-138.
  • 9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
  • 10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

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黑龙江大学自然科学学报
2013年 第4期

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