CONTENTS

Preface to the English Edition 

Preface to the Russian Edition

Introduction

1   Metric Spaces

1.1         Preliminaries

1.2         Some Metric Spaces of Functions

1.3         Energy Spaces   

1.4         Sets in a Metric Space

1.5         Convergence in a Metric Space

1.6         Completeness

1.7         The Completion Theorem

1.8         The Lebesgue Integral and the Space Lp

1.9         Banach and Hubert Spaces

1.10     Some Energy Spaces

1.11     Sobolev Spaces

1.12     Introduction to Operators

1.13     Contraction Mapping Principle

1.14     Generalized Solutions in Mechanics

1.15     Separability 62

1.16     Compactness, Hausdorff Criterion.     

1.17     Arzela's Theorem and Its Applications

1.18     Approximation Theory

1.19     Decomposition Theorem, Riesz Representation

1.20     Existence of Energy Solutions

1.21     The Problem of Elastico-Plasticity

1.22     Bases and Complete Systems

1.23     Weak Convergence in a Hubert Space

1.24     Ritz and Bubnov-Galerkin Methods  

1.25     Curvilinear Coordinates, Non-Homogeneous Boundary Conditions

1.26  The Bramble-Hilbert Lemma and Its Applications

2    Elements of the Theory of Operators 

2.1         Spaces of Linear Operators

2.2     Banach-Steinhaus Principle

2.3         The Inverse Operator

2.4     Closed Operators

2.5     The Notion of Adjoint Operator

2.6     Compact Operators

2.7     Compact Operators in Hilbert Space

2.8     Functions Taking Values in a Banach Space

2.9     Spectrum of Linear Operators

2.10  Resolvent Set of a Closed Linear Operator

2.11     Spectrum of Compact Operators in Hilbert Space

2.12Analytic Nature of the Resolvent of a Compact Linear Operator

2.13  Spectrum of Holomorphic Compact Operator Function

2.14  Spectrum of Self-Adjoint Compact Linear Operator in Hilbert Space

2.15     Some Applications of Spectral Theory

2.16     Courant's Mmimax Principle

3    Elements of Nonlinear Functional Analysis   

3.1         Frechet and Gateaux Derivatives

3.2         Liapunov-Schmidt Method

3.3     Critical Points of a Functional

3.4     Von Karman Equations of a Plate

3.5         Buckling of a Thin Elastic Shell

3.6     Equilibrium of Elastic Shallow Shells

3.7     Degree Theory

3.8         Steady-State Flow of Viscous Liquid

Appendix: Hints for Selected Problems

References