On the existence of positive solution for a kind of multi-point boundary value problem at resonance (Q965032)

The paper deals with the existence of positive solutions for a second-order multi-point boundary value problem at resonance \[ x''(t)+f(t,x(t))=0, \quad t\in (0,1), \] \[ x(0)=\sum_{i=1}^{m-2}\alpha_{i}x(\xi_{i}), \quad x(1)=\sum_{i=1}^{m-2}\beta_{i}x(\xi_{i}). \] The key tool is the Leggett-Williams norm-type theorem for coincidence equations due to \textit{D. O'Regan} and \textit{M. Zima} [Arch. Math. 87, No.~3, 233--244 (2006; Zbl 1109.47051)]. Reviewer's remark: There is a gap in the proof of one of the main results of the paper. Namely, the assumptions of Theorem 2 do not imply the condition (C2) of Lemma 2.1.