Linear and Nonlinear Functional Analysis with Applications, Second Edition, by Philippe G. Ciarlet, is a comprehensive 2025 treatment of functional analysis, spanning more than 1,240 pages. It begins with a review of real analysis and develops the theory of normed spaces, Banach spaces, inner-product and Hilbert spaces, and the major theorems of linear functional analysis, including the Hahn–Banach and Baire theorems.
The second edition substantially expands the original, adding more than 450 pages and over 210 problems, as well as new chapters on locally convex spaces, distributions, Fourier transforms, and Calderón–Zygmund singular integral operators.
The latter half moves into nonlinear functional analysis and its applications. It develops differential calculus in infinite-dimensional spaces, then applies the theory to linear and nonlinear partial differential equations, differential geometry, calculus of variations, and topological degree theory, including Brouwer and Leray–Schauder degree.
A major theme is the connection between abstract functional-analytic structures and concrete problems in PDEs and numerical analysis, with the author providing detailed proofs throughout. Overall, the book is designed as both an advanced textbook and a reference for graduate students, mathematicians, and researchers working with analysis and differential equations.
BOOK
The second edition substantially expands the original, adding more than 450 pages and over 210 problems, as well as new chapters on locally convex spaces, distributions, Fourier transforms, and Calderón–Zygmund singular integral operators.
The latter half moves into nonlinear functional analysis and its applications. It develops differential calculus in infinite-dimensional spaces, then applies the theory to linear and nonlinear partial differential equations, differential geometry, calculus of variations, and topological degree theory, including Brouwer and Leray–Schauder degree.
A major theme is the connection between abstract functional-analytic structures and concrete problems in PDEs and numerical analysis, with the author providing detailed proofs throughout. Overall, the book is designed as both an advanced textbook and a reference for graduate students, mathematicians, and researchers working with analysis and differential equations.
BOOK
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