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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 non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained. It combines classical and modern ideas to build a bridge between the language and thoughts of physicists and mathematicians. Many exercises and a comprehensive bibliography complement the text.

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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

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