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