Make sure to check the general databases for research on classics & ancient studies - they're very interdisciplinary, and thus may serve your research purposes well!
If we don't have access to an article or book chapter you need, you can place an interlibrary loan (ILL) request for it! Including as much information about the resource as you can, especially the ISSN, will help speed the process.
There are two ways to place an ILL request for an article:
1. From the e-link page of an article (click images for larger versions)
2. Via the ILL page on Columbia's site (click images for larger versions). Choose your institution, and then log-in with your UNI to request an article. If it's your first time logging in, you'll have to fill out some contact information initially.