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000722722 020__ $$a9783319117942$$qelectronic book
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000722722 0247_ $$a10.1007/978-3-319-11794-2$$2doi
000722722 035__ $$aSP(OCoLC)ocn897741943
000722722 035__ $$aSP(OCoLC)897741943
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000722722 08204 $$a515/.7$$223
000722722 1001_ $$aBrown, Robert F.,$$d1935-$$eauthor.
000722722 24512 $$aA topological introduction to nonlinear analysis$$h[electronic resource] /$$cRobert F. Brown.
000722722 250__ $$aThird edition.
000722722 264_1 $$aCham :$$bBirkhäuser,$$c2014.
000722722 300__ $$a1 online resource (x, 240 pages) :$$billustrations
000722722 336__ $$atext$$btxt$$2rdacontent
000722722 337__ $$acomputer$$bc$$2rdamedia
000722722 338__ $$aonline resource$$bcr$$2rdacarrier
000722722 504__ $$aIncludes bibliographical references and index.
000722722 5050_ $$aPreface -- Part I Fixed Point Existence Theory -- The Topological Point of View -- Ascoli-Arzela Theory -- Brouwer Fixed Point Theory -- Schauder Fixed Point Theory -- The Forced Pendulum -- Equilibrium Heat Distribution -- Generalized Bernstain Theory -- Part II Degree Theory -- Brouwer Degree -- Properties of the Brouwer Degree -- Leray-Schauder Degree -- Properties of the Leray-Schauder Degree -- The Mawhin Operator -- The Pendulum Swings back -- Part III Fixed Point Index Theory -- A Retraction Theorum -- The Fixed Point Index -- The Tubulur Reactor -- Fixed Points in a Cone -- Eigenvalues and Eigenvectors -- Part IV Bifurcation Theory -- A Separation Theorem -- Compact Linear Operators -- The Degree Calculation -- The Krasnoselskii-Rabinowitz Theorem -- Nonlinear Strum Liouville Theory -- More Strum Liouville Theory -- Euler Buckling -- Part V Appendices.
000722722 506__ $$aAccess limited to authorized users.
000722722 520__ $$aThis third edition of A Topological Introduction to Nonlinear Analysis is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. For this third edition, several new chapters present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding. "For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience."-Monatshefte fur Mathematik (2006)
000722722 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed December 8, 2014).
000722722 650_0 $$aNonlinear theories.
000722722 650_0 $$aNonlinear functional analysis.
000722722 77608 $$iPrint version:$$z9783319117935
000722722 852__ $$bebk
000722722 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-11794-2$$zOnline Access$$91397441.1
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