Linear and Nonlinear Functional Analysis with Applications

This new, considerably expanded edition covers the fundamentals of linear and nonlinear functional analysis, including distribution theory, harmonic analysis, differential geometry, calculus of variations, and degree theory. Numerous applications are included, especially to linear and nonlinear partial differential equations and to numerical analysis. All the basic theorems are provided with complete and detailed proofs. The author has added more than 450 pages of new material and more than 210 problems. The solutions to all of the problems will be made available on an accompanying website. Two entirely new chapters, one on locally convex spaces and distribution theory and the other on the Fourier transform and Calderón-Zygmund singular integral operators, have also been added. In addition, the chapter on the "great theorems" of nonlinear functional analysis has been enlarged and split into two chapters, one on the calculus of variations and the other on Brouwer's theorem, Brouwer's degree, and Leray-Schauder's degree. Audience Ideal for both teaching and self-study, Linear and Nonlinear Functional Analysis with Applications, Second Edition is intended for advanced undergraduate and graduate students in mathematics, university professors, and researchers. It is also an ideal basis for several courses on linear or nonlinear functional analysis.