# Nonlinear Functional Analysis

Springer Science & Business Media, 2013 M11 11 - 450 páginas
topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical language and way of thinking, one which is no doubt familiar from elementary lectures in analysis that did not worry much about its connections with algebra and topology. Of course we shall use some elementary topological concepts, which may be new, but in fact only a few remarks here and there pertain to algebraic or differential topological concepts and methods.

### Contenido

 Topological Degree in Finite Dimensions 1 Construction of the Degree 12 Concluding Remarks 27 8 33 Compact Maps 55 7 62 Set Contractions 68 Concluding Remarks 87
 Approximate Solutions 256 AProper Maps and Galerkin for Differential Equations 267 Exercises 275 Multis 278 13 287 16 298 Multis and Compactness 299 Extremal Problems 319

 Borsuks Theorem 90 Monotone and Accretive Operators 95 Monotone Operators on Banach Spaces 111 Accretive Operators 123 Concluding Remarks 133 Implicit Functions and Problems at Resonance 146 Problems at Resonance 172 Fixed Point Theory 186 Fixed Point Theorems Involving Compactness 203 Solutions in Cones 217 Solutions in Cones 238
 Exercises 329 Extrema Under Constraints 332 17 340 Critical Points of Functionals 349 Bifurcation 378 Global Bifurcation 398 Further Topics in Bifurcation Theory 411 Epilogue 426 Symbols 445 Derechos de autor