导语

  

内容提要

  

    陈鹏玉、李永祥、张旭萍著的《抽象发展方程非局部问题的可解性及其应用(英文版)》系统介绍了研究抽象发展方程非局部问题的基本思想、基本方法。通过阅读本书可以尽快的将初学者引入抽象发展方程非局部问题的研究领域，并接触到这一领域的研究前沿。此外，本书的研究工作对非线性分析与抽象空间微分方程理论及算子半群理论的结合有巨大的推动作用。

Chapter 1 Introduction and Background
  1.1 Nonlocal problem of abstract evolution equations
  1.2 Monotone iterative method based on lower and upper solutions
  1.3 Impulsive di.erential equations
  1.4 Fractional di.erential equations
  1.5 Non-autonomous evulution equations
  1.6 Nonlocal evolution equations with delay
  Reference
Chapter 2 Basic Definitions and Theorems
  2.1 Theory of operator semigroups
  2.2 Measure of noncompactness
  2.3 Fixed point theorems
  2.4 Cone and partial order
  2.5 Basic properties of fractional integral and derivative
  Reference
Chapter 3 Strong Solutions for Nonlocal Evolution Equations
  3.1 Existence and uniqueness of strong solutions for semilinear evolution equations with nonlocal initial conditions
  3.2 Regularity for evolution equations with nonlocal initial conditions on infinite interval
  3.3 Asymptotic stability of strong solutions for evolution equations with nonlocal initial conditions
  3.4 Notes
  Reference
Chapter 4 Monotone Iterative Method Based on Lower and Upper Solutions
  4.1 Monotone iterative technique for semilinear evolution equations with nonlocal initial conditions
  4.2 Perturbation method for nonlocal evolution equations with instantaneous impulses
    4.2.1 Initial value problem of linear evolution equations
    4.2.2 g is compact in PC(J;E)
    4.2.3 g is continuous in PC(J;E)
    4.2.4 The case of lower and upper solutions do not exist
    4.2.5 Applications
  4.3 Iterative method for a new class of evolution equations with non- instantaneous impulses
    4.3.1 Linear evolution equation with non-instantaneous impulses
    4.3.2 T(·) and gk are compact
    4.3.3 T(·) is not compact, gk is compact
    4.3.4 T(·) and gk are not compact
    4.3.5 Applications
  4.4 Notes
    Reference
Chapter 5 Nonlocal Evolution Equation of Fractional Order
  5.1 Fractional evolution equations with nonlocal conditions and noncompact semigroup
  5.2 Nonlocal problem for fractional evolution equations of mixed type
    5.2.1 Existence of mild solutions
    5.2.2 Existence of positive mild solutions
  5.3 Fractional evolution equations with mixed monotone nonlocal conditions
    5.3.1 T(t) is compact for t > 0
    5.3.2 T(t)(t > 0) is a C0-semigroup
    5.3.3 Existence of mild solution
    5.3.4 Applications
  5.4 Notes
  Reference
Chapter 6 Fractional Non-autonomous Evolution Equations
  6.1 Fractional non-autonomous evolution equation with nonlocal conditions
  6.2 Application
  6.3 Notes and comments
  Reference
Chapter 7 Nonlocal Evolution Equation with Delay
  7.1 Existence of solutions for delay evolution equations with nonlocal conditions
    7.1.1 Existence results under the situation that g is Lipschitz continuous
    7.1.2 Existence results under the situation that g is compact
    7.1.3 An example
  7.2 Neutral delay evolution equations with mixed nonlocal plus local initial conditions
    7.2.1 Existence of mild solutions
    7.2.2 The regularity of solutions
    7.2.3 An example
  7.3 Fractional retarded evolution equations subjected to mixed nonlocal plus local initial conditions
    7.3.1 Existence of mild solutions
    7.3.2 Existence of positive mild solutions
    7.3.3 An example
  7.4 Notes
  Reference
Index