Applied nonlinear functional analysis. An introduction (Q6566915)

The first edition of this rich, but densely written textbook was reviewed in [Zbl 1404.46001]. For the second edition, the authors have added, apart from the usual updates, new sections on Hausdorff measures, semigroups of operators, Musielak-Orlicz spaces (called generalised Orlicz spaces here), and on various nonlinear operators and inequalities that are important in applications (e.g., the \(p\)-Laplacian and Hardy type inequalities).\N\NIt seems that the book would have benefitted from another round of proof-reading; there are a number of typos (both significant ones, e.g., in Proposition~2.8.11, and insignificant ones, e.g., in the definition of \(C\) on page~173), missing assumptions (e.g., Proposition~2.8.14) and incomplete proofs (e.g., the argument of Remark~4.8.2 falls short of proving left-continuity for which one needs Proposition~4.8.4). Also, the reader is left with guessing how to deduce, say, Corollary~4.8.9 from Corollary~4.8.7 (a single additional line could have clarified the matter).\N\NHaving said that, I would still like to emphasise that the authors have succeeded in covering a tremendous amount of material in this volume that is suitable for advanced students.