Synopsis
Preface. Notation. Overview. I: Fixed Point Methods. 1. Compactness in Metric Spaces. 2. Completely Continuous Operators on Banach Spaces. 3. Continuous Solutions of Integral Equations via Schauder's Theorem. 4. The Leray-Schauder Principle and Applications. 5. Existence Theory in LP Spaces. References: Part I. II: Variational Methods. 6. Positive Self-Adjoint Operators in Hilbert Spaces. 7. The Fréchet Derivative and Critical Points of Extremum. 8. The Mountain Pass Theorem and Critical Points of Saddle Type. 9. Nontrivial Solutions of Abstract Hammerstein Equations. References Part II. III: Iterative Methods. 10. The Discrete Continuation Principle. 11. Monotone Iterative Methods. 12. Quadratically Convergent Methods. References: Part III. Index.
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