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非自治算子微分方程与积微分方程的若干问题
  • 项目名称：非自治算子微分方程与积微分方程的若干问题
  • 项目类别：面上项目
  • 批准号：10771202
  • 申请代码：A0106
  • 项目来源：国家自然科学基金
  • 研究期限：2008-01-01-2010-12-31
  • 项目负责人：梁进
  • 负责人职称：教授
  • 依托单位：上海交通大学
  • 批准年度：2007
中文摘要：

在本研究中，我们揭示了Hille-Yosida算子的一些深刻性质；在相当广泛的情形下，论证了Robin边值条件控制的二阶微分算子生成强连续的余弦算子族；建立了简明适用的判别Banach空间中非线性算子积微分方程非局部Cauchy问题温和解存在唯一的法则；对非自治算子微分方程的非线性项不具有Lipschitz估计的情形，获得了简明的拟概自守解存在性定理；得到了更广泛适用关于半线性非自治反应扩散系统的比较原理；获得了判断抽象Volterra 型方程的解的一致指数稳定性的新法则，给出了新型的、条件宽松的非线性算子的随机耦合定理；明确揭示了Banach空间值加权概自守函数的分解一般不是唯一的；解答了Banach空间值加权概自守函数理论中的一些基本问题；揭示了算子半群的深层次性质；建立了关于混合单调算子的相当一般的不动点定理；还建立了一系列其他研究结果。在《Trans. Amer. Math. Soc.》、《J.Funct. Anal.》、《J. Evol. Equ. 》等期刊上发表论文38篇，被SCI、EI收录45篇(含双录的)。培养博士后2人，博士生7人, 硕士生2人。

中文主题词： 无穷维空间、线性与非线性算子
结论摘要：

英文主题词infinite dimensional space, linear and nonlinear operators

成果综合统计
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  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
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期刊论文
Convergence theorems of new Ishikawa iterative procedures with errors for multi-valued $\Phi$-hemico
Multiple positive solutions for second order impulsive boundary value problems in Banach spaces
Solutions to Fractional Differential Equations with Nonlocal Initial Condition in Banach Spaces
Almost Automorphic Solutions to Abstract Fractional Differential Equations
Notes on the Propagators of Evolution Equations
Iterative Algorithms with Variable Coefficients for Asymptotically Strict Pseudocontractions
Fixed Point Theorems for Nonlinear Operators with and without Monotonicity in Partially Ordered Bana
Decomposition of weighted pseudo-almost periodic functions
Almost automorphic solutions to nonautonomous semilinear evolution equations in Banach spaces
Iterative approximation problems of fixed points for asymptotically pseudo-contractive mappings
Multiple Positive Periodic Solutions for Delay Differential System
Positive Solutions to Singular and Delay Higher-Order Differential Equations on Time Scales
Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications
Some properties of pseudo-almost automorphic functions and applications to abstract differential equ
Existence of positive almost automorphic solutions to nonlinear delay integral equations
Nonlocal impulsive problems for nonlinear differential equations in Banach spaces
Nonlocal impulsive problems for integrodifferential equations
Positive almost automorphic solutions for a class of non-linear delay integral equations
Blow-up and global existence of solutions to integral equations with infinite delay in Banach spaces
Uniform exponential stability of solutions to abstract Volterra equations
RANDOM COINCIDENCE POINTS AND RANDOM FIXED POINTS OF MULTIFUNCTIONS IN METRIC SPACES
Asymptotic stability of the zero solution for degenerate retarded differential equations
Some properties of Stepanov-like almost automorphic functions and applications to abstract evolution
A new stability criterion for polynomials with the quasi-critical condition
Existence of positive almost automorphic solutions to neutral nonlinear integral equations
Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal ini
Composition of pseudo almost automorphic and asymptotically almost automorphic functions
Approximation theorems for the propagators of higher order abstract cauchy problems
Coupled non-local periodic parabolic systems with time delays
A note on almost automorphic functions
Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions
Criteria on all-delay stability of degenerate differential systems
A perturbation theorem for local C-regularized cosine functions
Multiplicative perturbations of incomplete second order abstract differential equations
Existence of almost periodic solutions for SICNNs with time-varying delays
Second order differential operators with Feller-Wentzell type boundary conditions
Nonlocal problems for integrodifferential equations
会议论文
On a comparison principle for delay coupled systems with nonlocal and nonlinear boundary conditions
梁进的项目
Banach空间中几类非线性算子微分系统的解及相关基本理论的构建
Banach空间中非线性微分与积微分方程的若干研究
期刊论文 33