The authors attempt to use coincidence degree theory to study the th-order multipoint boundary value problems at resonance
The idea in Mawhin’s coincidence degree theory is to find a Fredholm map of index 0, and two continuous projectors and such that and . Furthermore, one needs a map that is -compact on a closed subset of where . For the first existence theorem, the authors take and and define the operator by , with : , , and define by . The first boundary value problem can then be written as . There is a subtle flaw in their arguments in the first existence theorem when . They define the operator by
This is not a projector if . Note that
The theorems are valid in the case when .