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