Solvability of a higher-order multi-point boundary value problem at a resonance. (Q664410)

Sufficient conditions for the existence of solutions of a multi-point boundary value problem for an \(n\)-th order ordinary differential equation with a general right-hand side are given. The authors focus on the case when \(\text{dim ker }L=2\), where \(L\) is related to the linear equation \(Lx:=x^{(n)}(t)=0\). Mawhin's coincidence degree theory is applied for this aim. An illustrative example for a concrete third-order equation is supplied.