Comment on the article ``On the existence of the N-body Efimov effect'' by X.P. Wang (Q447921)

The author considers the Efimov effect for the \(N\)-body problem with \(N\geq 4\) for the Schrödinger equation in \({\mathbb R}{^ 3},\) where the potential consists of the sum of two-body interaction terms depending only on the separation distance. Under appropriate restrictions, it is shown that there may be an infinite number of discrete eigenvalues below \(E_ 0\) for the whole system as a result of the contributions from the eigenvalues and resonances at \(E_ 0\) of the \((N-1)\)-particle system, where \(E_ 0\) is the threshold energy separating the discrete and continuous spectra. The proof uses the ideas from \textit{A. V. Sobolev} [Commun. Math. Phys. 156, No. 1, 101--126 (1993; Zbl 0785.35070)] and exploits the conditions on the finiteness of number of discrete eigenvalues by \textit{W. D. Evans} and \textit{R. T. Lewis} [Trans. Am. Math. Soc. 322, No. 2, 593--626 (1990; Zbl 0732.35062)].