Nonlinear Functional Analysis
Courier Corporation, 2013 M10 9 - 464 páginas
Hailed 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.
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A-proper accretive algebraic apply assume bifurcation point boundary value problem bounded sets chapter choose closed convex cone convergent convex functional convex set deﬁned deﬁnition degree theory differential equations eigenvalue equivalent example Exercise exists F x0 ﬁeld ﬁnd ﬁnite ﬁnite-dimensional ﬁrst ﬁxed point ﬁxed point theorem Fredholm operators function Furthermore given go(x Hence Hilbert space Hint homeomorphism homotopy hyperaccretive hypermaximal implicit function theorem implies inﬁnite Lemma Let F let us consider let us prove lower semicontinuous maximal monotone metric space multis neighbourhood nonexpansive nonlinear norm notice open bounded proof to Theorem properties Proposition real Banach space reﬂexive remarks result satisﬁes satisfying semicontinuous semigroup Stanislaw Jerzy Lec strictly convex subset subspace sufﬁciently small Suppose topological trivial uniformly convex unique solution weakly yields zero