This is the fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the nonspecialist. This book attempts to combine classical and modern ideas and to build a bridge between the language and thoughts of physicists and mathematicians. This corrected printing is fully revised and contains a new section of additional references along with many exercises.

Preface; Preface to Second Corrected Printing; Translator's Preface; Introduction: Mathematics and Physics; APPLICATIONS IN MECHANICS: Basic Equations of Point Mechanics; Dualism Between Wave and Particle, Preview of Quantum Theory, and Elementary Particles; APPLICATIONS IN ELASTICITY THEORY: Elastoplastic Wire; Basic Equations of Nonlinear Elasticity Theory; Monotone Potential Operators and a Class of Models with Nonlinear Hooke's Law, Duality and Plasticity, and Polyconvexity; Variational Inequalities and the Signorini Problem for Nonlinear Material; Bifurcation for Variational Inequalities; Pseudomonotone Operators, Bifurcation, and the von K rm n Plate Equations; Convex Analysis, Maximal Monotone Operators, and Elasto-Viscoplastic Material with Linear Hardening and Hysteresis; APPLICATIONS IN THERMODYNAMICS: Phenomenological Thermodynamics of Quasi-Equilibrium and Equilibrium States; Statistical Physics; Continuation with Respect to a Parameter and a Radiation Problem of Carleman;APPLICATIONS IN HYDRODYNAMICS: Basic Equations of Hydrodynamics; Bifurcation and Permanent Gravitational Waves; Viscoud Fluids and the Navier-Stokes Equations; MANIFOLDS AND THEIR APPLICATIONS: Banach Manifolds; Classical Surface