Nonlinear Functional Analysis and Its Applications, Part 4

Contents

Preface
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

• 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

• Phenomenological Thermodynamics of Quasi-Equilibrium and Equilibrium States
• Statistical Physics
• Continuation with Respect to a Parameter and a Radiation Problem of Carleman

• Basic Equations of Hydrodynamics
• Bifurcation and Permanent Gravitational Waves
• Viscoud Fluids and the Navier-Stokes Equations

• Banach Manifolds
• Classical Surface Theory, the Theorema Egregium of Gauss, and Differential Geometry on Manifolds
• Special Theory of Relativity
• General Theory of Relativity
• Simplicial Methods, Fixed Point Theory, and Mathematical Economics
• Homotopy Methods and One-Dimensional Manifolds
• Dynamical Stability and Bifurcation in B-Spaces