Nonlinear Functional AnalysisHailed as "eminently suitable as a text for a graduate course" by the Bulletin of the American Mathematical Society, this volume offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It offers extensive commentary and many examples in addition to an abundance of interesting, challenging exercises. Starting with coverage of the development of the Brower degree and its applications, the text proceeds to examinations of degree mappings for infinite dimensional spaces and surveys of monotone and accretive mappings. Subsequent chapters explore the inverse function theory, the implicit function theory, and Newton's methods as well as fixed-point theory, solutions to cones, and the Galerkin method of studying nonlinear equations. The final chapters address extremal problems—including convexity, Lagrange multipliers, and mini-max theorems—and offer an introduction into bifurcation theory. Suitable for graduate-level mathematics courses, this volume also serves as a reference for professionals. |
Other editions - View all
Common terms and phrases
A-proper A₁ accretive B₁ bifurcation point bounded sets choose closed convex compact cone consider continuous conv convergent convex functional convex set D₁ defined differential equations eigenvalue example Exercise exists F₁ finite fixed point theorem Fredholm operators function given Hence Hilbert space Hint homeomorphism implicit function theorem implies K₁ Let F let us prove linear Lipschitz lower semicontinuous M₁ maximal monotone metric neighbourhood nonexpansive nonlinear norm open bounded P₁ properties Proposition R₁ real Banach space reflexive result satisfies semicontinuous semigroup Stanislaw Jerzy Lec subset subspace Suppose T₁ topological uniformly convex w-periodic solution x₁ Xn+1 y₁ zero λ₁ λη λο Ω₁