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
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