变分方法及应用PDF电子书下载

Chapter 1　Preliminaries 1

1.1 Sobolev Spaces 1

1.2　Differential Functionals 6

1.3　The(PS)Conditions 12

1.4 Weak Solutions 13

1.5 Concentration-Compactness Principle 17

Chapter 2　Superlinear Variational Problems 25

2.1 Generalized Kadomtsev-Petviashvili Equations 25

2.2 Quasilinear Elliptic Equations with Nonlinear Boundary Conditions 33

2.3 A Superlinear Boundary Value Problem 46

2.4 Elliptic Systems with Nonlinear Boundary Conditions 58

Chapter 3 Singular Brezis-Nirenberg Problems 77

3.1 Multiple Solutions of Brezis-Nirenberg Problems 77

3.2 Quasilinear Brezis-Nirenberg Type Problems 85

Chapter 4 On Kirehhoff-Type Problems 101

4.1 Kirchhoff-Type Equations with Parameters 101

4.2 Multiple Solutions of Kirchhoff-Type Problems 111

Chapter 5 Noncompact Variational Problems 121

5.1 Critical Elliptic Equations in RN 121

5.2 Sublinear Critical Elliptic Problems 136

5.3 Critical Semilinear Elliptic Equations 147

Bibliography 167