This work is concerned with solvability of the multipoint boundary value problem
where , , , , , and is a Carathéodory function. The additional assumptions
are “critical”, that is, responsible for resonance.
This note complements the result by N. Kosmatov [Nonlinear Anal., Theory Methods Appl. 65, 622–633 (2006; Zbl 1121.34023)] and extends the result by the first author [Appl. Math. Comput. 143, 275–299 (2003; Zbl 1071.34014)]. The existence result follows from the celebrated coincidence degree theorem due to J. Mawhin [Topological degree methods in nonlinear boundary value problems (Regional Conference Series in Mathematics, No. 40, Providence, R.I., The American Mathematical Society) (1979; Zbl 0414.34025)].