微分方程边值问题具有悠久的研究历史，是微分方程理论的一个重要分支。目前，国内外主要研究各类边值问题的解的存在性和唯一性、多解存在性、正解存在性，为具体问题的求解提供理论基础，这提供了研究微分方程边值问题的必要性。研究微分方程边值问题的解的存在性理论的传统方法有：拓扑度理论、上下解方法。变分法越来越多地应用在解存在性研究中，逐渐成为研究非线性微分方程的主要工具，此方法能得到不同于其他传统方法的结果。
本书介绍变分法的主要结论和最新进展，以及如何应用变分法到微分方程、脉冲微分方程、差分方程定解问题中，得到解的存在性、多解性、变号解和正解存在性。为了进一步研究解的性态，介绍了如何将变分法与上下解方法结合得到变号解存在性。这些研究丰富了解的存在性理论，扩展了变分法的应用范围。

CHAPTER 1 Nonlinear Differential Equations and Difference Equations
1.1 Differential equations
1.2 Impulsive differential equations
1.3 Difference equations
Bibliography
CHAPTER 2 Variational Approach
2.1 Gateaux derivative and Frechet derivative
2.2 Lower semi-continuous functions
2.3 Mountain pass theorem and variant
2.4 Morse theory
2.5 Some critical point theorems
2.6 Three critical points theorem
2.7 Nonsmooth analysis
2.8 Sobolev space
2.9 Some basic results
Bibliography
CHAPTER 3 Ordinary Differential Equations
3.1 Periodic solutions for differential equation systems with a p-Laplacian
3.2 Anti-periodic solutions for a gradient system with resonance
3.3 Anti-periodic boundary value problem with non-resonance
3.4 2n-order differential equation
3.5 Notes and comments
Bibliography
CHAPTER 4 Impulsive Differential Equations
4.1 Mixed boundary value problem for impulsive differential equation
4.2 Sturm-Liouville boundary value problem for impulsive differential equations.
4.2.1 Impulsive linear problem
4.2.2 Impulsive nonlinear problem
4.3 Impulsive differential equations with p-Laplace operator
4.4 Sign-changing solutions for impulsive differential equations(I)
4.4.1 Basic lemmas for the case α, γ＞0
4.4.2 Main results for the case α, γ＞0
4.4.3 For the case α, γ≥0
4.5 Sign-changing solutions for impulsive differential equations (II)
4.5.1 Four solutions for α, γ＞0
4.5.2 Four solutions for α, γ≥0
4.6 Fourth-order impulsive boundary value problem
4.6.1 Existence results for one solution and infinitely many solutions
4.6.2 Exsitence results for three positive solutions
4.6.3 Existence results for infinitely many solutions
4.7 Impulsive differential inclusion
4.7.1 Variational structure and related lemmas
4.7.2 Existence results for three solutions
4.8 Notes and comments
Bibliography
CHAPTER 5 Difference Equations
5.1 Discrete Sturm-Liouville problem with a p-Laplacian
5.1.1 For the case 1
5.1.2 For the case 2-case 4
5.2 Difference equation with Neumann boundary conditions
5.3 2n-order difference equation
5.4 Notes and comments
Bibliography