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This book describes many new results and extensions of the theory of generalised topological degree for densely defined A-proper operators and presents important applications, particularly to boundary value problems of non-linear ordinary and partial differential equations, which are intractable under any other existing theory. A-proper mappings arise naturally in the solution to an equation in infinite dimensional space via the finite dimensional approximation. This theory subsumes classical theory involving compact vector fields, as well as the more recent theories of condensing vector-fields, strongly monotone and strongly accretive maps. Researchers and graduate students in mathematics, applied mathematics and physics who make use of non-linear analysis will find this an important resource for new techniques.

Topological degree. --- Boundary value problems.

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"The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can " [Publisher]

Algebraic topology. --- Topologie algébrique. --- Topological degree. --- Degré topologique. --- Homotopy theory. --- Homotopie.

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Banach [Espaces de ] --- Banach [Ruimten van ] --- Banach spaces --- Degree [Topological ] --- Degres topologiques --- Graden [Topologische ] --- Degree, Topological --- Banach, Espaces de --- Degré topologique --- Topological degree --- Topological degree. --- Degré topologique --- Algebraic topology --- Topologie algébrique --- Degré topologique. --- Analyse fonctionnelle non linéaire --- Nonlinear functional analysis --- Topologie algébrique --- Degré topologique. --- Analyse fonctionnelle non linéaire. --- Nonlinear functional analysis. --- Point fixe, Théorème du

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Equations. --- Nonlinear theories. --- Topological degree. --- Équations. --- Théories non linéaires --- Degré topologique --- Analyse fonctionnelle non linéaire --- Nonlinear functional analysis. --- Equations integrales non-lineaires --- Equations integrales non-lineaires

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Operator theory --- Differential equations --- Nonlinear boundary value problems --- Topological degree --- Degree, Topological --- Degree (Topology) --- Degree theory --- Differential equations, Functional --- Functional differential equations --- 517.91 --- Algebraic topology --- Boundary value problems --- Differential equations, Nonlinear --- Functional equations --- 517.91 Ordinary differential equations: general theory --- Ordinary differential equations: general theory --- Topologie algébrique --- Topological degree. --- Degré topologique. --- Équations différentielles non linéaires --- Équations différentielles non linéaires --- Analyse fonctionnelle non linéaire --- Nonlinear functional analysis --- Topologie algébrique --- Degré topologique. --- Analyse fonctionnelle non linéaire. --- Nonlinear boundary value problems. --- Functional differential equations. --- Équations différentielles non linéaires.