变分法pdf电子书版本下载

点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
种子下载[BT下载速度快] 温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页 直链下载[便捷但速度慢]   [在线试读本书]   [在线获取解压码]

变分法PDF格式电子书版下载

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如 BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数 要大于 标注页数，上中下等多册电子书除外）

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

Chapter Ⅰ．The Direct Methods in the Calculus of Variations 1

1．Lower Semi-Continuity 2

Degenerate Elliptic Equations 4

Minimal Partitioning Hypersurfaces 6

Minimal Hypersurfaces in Riemannian Manifolds 7

A General Lower Semi-Continuity Result 8

2．Constraints 13

Semi-Linear Elliptic Boundary Value Problems 14

Perron's Method in a Variational Guise 16

The Classical Plateau Problem 19

3．Compensated Compactness 25

Applications in Elasticity 29

Convergence Results for Nonlinear Elliptic Equations 32

Hardy space methods 35

4．The Concentration-Compactness Principle 36

Existence of Extremal Functions for Sobolev Embeddings 42

5．Ekeland's Variational Principle 51

Existence of Minimizers for Quasi-Convex Functionals 54

6．Duality 57

Hamiltonian Systems 60

Periodic Solutions of Nonlinear Wave-Equations 65

7．Minimization Problems Depending on Parameters 69

Harmonic maps with singularities 71

Chapter Ⅱ．Minimax Methods 74

1．The Finite Dimensional Case 74

2．The Palais-Smale Condition 77

3．A General Deformation Lemma 81

Pseudo-Gradient Flows on Banach Spaces 81

Pseudo-Gradient Flows on Manifolds 85

4．The Minimax Principle 87

Closed Geodesics on Spheres 89

5．Index Theory 94

Krasnoselskii Genus 94

Minimax Principles for Even Functionals 96

Applications to Semilinear Elliptic Problems 98

General Index Theories 99

Ljusternik-Schnirelman Category 100

A Geometrical S1-Index 101

Multiple Periodic Orbits of Hamiltonian Systems 103

6．The Mountain Pass Lemma and its Variants 108

Applications to Semilinear Elliptic Boundary Value Problems 110

The Symmetric Mountain Pass Lemma 112

Application to Semilinear Equations with Symmetry 116

7．Perturbation Theory 118

Applications to Semilinear Elliptic Equations 120

8．Linking 125

Applications to Semilinear Elliptic Equations 128

Applications to Hamil-tonian Systems 130

9．Parameter Dependence 137

10．Critical Points of Mountain Pass Type 143

Multiple Solutions of Coercive Elliptic Problems 147

11．Non-Differentiable Functionals 150

12．Ljusternik-Schnirelman Theory on Convex Sets 162

Applications to Semilinear Elliptic Boundary Value Problems 166

Chapter Ⅲ．Limit Cases of the Palais-Smale Condition 169

1．Poho？aev's Non-Existence Result 170

2．The Brezis-Nirenberg Result 173

Constrained Minimization 174

The Unconstrained Case:Local Compact-ness 175

Multiple Solutions 180

3．The Effect of Topology 183

A Global Compactness Result 184

Positive Solutions on Annular-Shaped Regions 190

4．The Yamabe Problem 193

5．The Dirichlet Problem for the Equation of Constant Mean Curvature 203

Small Solutions 204

The Volume Functional 206

Wente's Uniqueness Result 208

Local Compactness 209

Large Solutions 212

6．Harmonic Maps of Riemannian Surfaces 214

The Euler-Lagrange Equations for Harmonic Maps 215

Bochner identity 217

The Homotopy Problem and its Functional Analytic Setting 217

Existence and Non-Existence Results 220

The Evolution of Harmonic Maps 221

Appendix A 237

Sobolev Spaces 237

H？lder Spaces 238

Imbedding Theorems 238

Density Theorem 239

Trace and Extension Theorems239—Poincaré Inequality 240

Appendix B 242

Schauder Estimates 242

LP-Theory 242

Weak Solutions 243

A Reg-ularity Result 243

Maximum Principle 245

Weak Maximum Principle 246

Application 247

Appendix C 248

Fréchet Differentiability 248

Natural Growth Conditions 250

References 251

Index 271