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非局部条件下半线性微分方程的适度解 被引量：3

Mild Solutions for Semilinear Differential Equations with Nonlocal Conditions
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摘要 讨论了Banach空间中非局部条件下半线性微分方程的适度解的存在性,利用不动点和非紧测度的方法,给出了在不需要半群紧性条件下方程适度解的存在性,并且对f是连续紧算子和f是Lipschitz连续的情形做了统一处理,从而得到了更为广泛和一般性的结果. We discuss the existence of mild solutions for semilinear differential equations with nonlocal conditions in ganach spaces. By using the method of the fixed point and the measure of noncompacmess, the existence of mild solutions without the compactness of semigroup can be got and special cases as fis completely continuous and Lipschitz continuous can also be tackled, which are more extensive and general results.
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 《数学的实践与认识》 CSCD 北大核心 2009年第22期179-184,共6页 Mathematics in Practice and Theory
基金 国家自然科学基金(10971182) 淮阴工学院青年教师基金(HGC0929)
关键词 非局部条件 适度解 不动点 非紧测度 nonlocal eonditions mild solution fixed point measure of noncompactness
分类号 O175.6 [理学—基础数学]
  • 相关文献

参考文献10

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二级参考文献18

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共引文献66

同被引文献20

  • 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.
  • 3FAN Zhen-bin. Impulsive problems for semilinear differential equations with nonlocal conditions[J]. Nonlinear Anal: Theory, Methods & Appl, 2010, 72(2): 1104-1109.
  • 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.
  • 6I.IU James H. Nonlinear impulsive evolution equations[J]. Dyn Cont Discrete Impuls Syst, 1999, 6(1): 77-85.
  • 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.
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  • 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.

引证文献3

二级引证文献6

数学的实践与认识
2009年 第22期

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