## 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. |

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apply approximation assume assumption Banach space bifurcation bounded called chapter choose clear closed compact complete cone consequence consider constant contains continuous convergent convex corresponding deﬁned deﬁnition eigenvalue equivalent essential Evidently example Exercise exists extension fact ﬁnd ﬁnite ﬁrst ﬁxed point function Furthermore given gives Hence homeomorphism implies integral interesting Let X linear locally maps maximal means measurable mentioned methods metric monotone neighbourhood nonlinear norm normal Note Notice obtain open bounded operators particular positive problem projection Proof properties Proposition prove real Banach space remarks remember respect result satisﬁes satisfying simple solution subset sufﬁciently Suppose Theorem theory topological trivial uniformly unique usually write yields zero