In deep X-ray surveys, active galactic nuclei (AGNs) with a broad range of luminosities have been identified. However, cosmologically distant low-luminosity AGN (LLAGN, $L_{mathrm{X}} lesssim 10^{42}$ erg s$^{-1}$) identification still poses a challenge due to significant contamination from host galaxies. Based on the 7 Ms Chandra Deep Field-South (CDF-S) survey, the longest timescale ($sim 17$ years) deep X-ray survey to date, we utilize an X-ray variability selection technique to search for LLAGNs that remain unidentified among the CDF-S X-ray sources. We find 13 variable sources from 110 unclassified CDF-S X-ray sources. Except for one source which could be an ultraluminous X-ray source, the variability of the remaining 12 sources is most likely due to accreting supermassive black holes. These 12 AGN candidates have low intrinsic X-ray luminosities, with a median value of $7 times10^{40}$ erg s$^{-1}$. They are generally not heavily obscured, with an average effective power-law photon index of 1.8. The fraction of variable AGNs in the CDF-S is independent of X-ray luminosity and is only restricted by the total number of observed net counts, confirming previous findings that X-ray variability is a near-ubiquitous property of AGNs over a wide range of luminosities. There is an anti-correlation between X-ray luminosity and variability amplitude for high-luminosity AGNs, but as the luminosity drops to $lesssim 10^{42}$ erg s$^{-1}$, the variability amplitude no longer appears dependent on the luminosity. The entire observed luminosity-variability trend can be roughly reproduced by an empirical AGN variability model based on a broken power-law power spectral density function.
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