What books collect **examples** and **counterexamples** (or also "solved exercises", for some suitable definition of "exercise") in 

- real analysis,
- complex analysis,
- functional analysis, 
- ODEs,
- PDEs?

The only book of this kind that I know of is 
the famous 

> *Counterexamples in Analysis* by Bernard R. Gelbaum and John M. H. Olmsted.