  Single-particle resonances in the continuum are crucial for studies of exotic
nuclei. In this study, the Green's function approach is employed to search for
single-particle resonances based on the relativistic-mean-field model. Taking
$^{120}$Sn as an example, we identify single-particle resonances and determine
the energies and widths directly by probing the extrema of the Green's
functions. In contrast to the results found by exploring for the extremum of
the density of states proposed in our recent study [Chin. Phys. C, 44:084105
(2020)], which has proven to be very successful, the same resonances as well as
very close energies and widths are obtained. By comparing the Green's functions
plotted in different coordinate space sizes, we also found that the results
very slightly depend on the space size. These findings demonstrate that the
approach by exploring for the extremum of the Green's function is also very
reliable and effective for identifying resonant states, regardless of whether
they are wide or narrow.
