Perspectives in Nonlinearity: An Introduction to Nonlinear Analysis

Preface 
Chapter 1. Once Over Lightly 
1-1. Diophantine Equations and the Genus of an Algebraic Plane Curve 
1-2. Zeros and Critical Points of Analytic Functions of One Complex Variable 
1-3. Some General Problems of Nonlinear Analysis 
1-4. Applications of Nonlinear Problems 
Chapter 2. Finite Dimensional Systems in H 
2-1. The Definition of Degree of a Mapping 
2-2. Some Properties of the Degree of a Mapping 
2-3. Gradient Systems and Their Basic Properties 
2-^. Gradient Systems with Nondegenerate Critical Points 
2-5. Critical Points for General Gradient Systems 
2-6. Systems Deformable to Gradient Systems 
Chapter 3. Infinite Dimensional Systems 
3-1. The Degree of a Class of Operators in Spaces of Infinite Dimension 
3-2. A Special Class of Noncompact Operators 
3-3* Gradient Operators and Their Properties 
3-4. A Remark on the Theory of Critical Points of Infinite Dimensional Gradient Operators 
3-5. Local Behavior of Nonlinear Operator Equations in Hilbert Space 
Chapter 4* Applications 
4-1. Global Univalence 
4-2. Topics in Nonlinear Autonomous Ordinary Differential Equations 
4-3. Topics in Elliptic Partial Differential Equations 
Appendix I. The Axioms of Homology Theory 
Appendix II. Standard Results from Analysis