On a general variational framework for existence and uniqueness in differential equations (Q2127435)

The author of this well-written and illuminating paper first rephrases Banach's classical fixed point theorem in Banach spaces as a variational principle and then provides several examples which show, very convincingly, that his variational principle is helpful not only in the study of ordinary differential equations, but also in that of partial differential equations. These examples include Cauchy problems for ODEs, linear hyperbolic problems, nonlinear monotone PDEs, nonlinear wave models, and steady Navier-Stokes systems. \{Reviewer's remark: In connection with the author's variational proof of Banach's fixed point theorem, see also the argument on page 2 of the book by \textit{K. Goebel} and \textit{S. Reich} [Uniform convexity, hyperbolic geometry, and nonexpansive mappings. New York, NY: Marcel Dekker, Inc. (1984; Zbl 0537.46001)].\}