In addition to individual articles, the Electronic Journal of Differential Equations also publishes monographs in the area of differential equations. The first one was a book that I think I remember seeing on library bookshelves: Showalter’s Hilbert Space Methods for Differential Equations.
Ralph Showalter was my advisor. I spent a lot of time with his Hilbert space methods book. The first time I heard of using Hilbert space methods to prove PDE existence theorems it seemed like pulling a rabbit out of a hat.