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PREFACE ¡@This volume is intended as an essentially self-contained exposition of portions of the theory of nonlinear analysis. It grew out of lecture notes for graduate courses by the author at National Tsing Hua University, Hsinchu, Taiwan. ¡@For many decades, great mathematical interest has focused on problems associated with linear operators and the extension of the results of linear algebra to an in¡Ânite-dimensional context. When one drops the assumption of linearity, the associated operator theory and the many concrete problems associated with such a theory represent a frontier of mathematical research. Just as in the linear case, these results were inspired by and are highly relevant to concrete problems in mathematical analysis. We shall take up a variety of analytic and topological techniques for the study of nonlinear problems and their applicability to a variety of concrete problems taken from various ¡Âelds of mathematical analysis. ¡@This volume contains: function analysis; ¡Âxed point theorems in Banach spaces; calculus in Banach spaces; bifurcation theory for operators on Banach spaces; Sobolev spaces in R and in RN; N > 1; the theory of compact operators, Fredholm operators, and monotone operators; the variational methods for nonlinear equations; the topological degree of the compactness erturbation of the identity map; and the applications of topological degrees to ODEs and PDEs. ¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@Hwai-Chiuan Wang ¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@July 2003 |
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