Inherited tenants left before lease ran out. Do I have recourse?

[Joel Fine]

Seeking wisdom from the BP community.

I recently bought a 7-unit apartment building in Ohio. At the time of sale, some of the units were occupied by tenants who are on 1-year leases that have several months to go.

A couple of those tenants decided to skip town shortly after I bought the property, before their lease terms were up. They did not pay any rent to me. I don't know if they were current with the seller, but I think that's irrelevant.

Their leases obligate them to pay rent for another few months, but of course the leases only name the seller of the property, not me.

Do I have recourse to go after them for the remainder of their leases? Even if I do, is the pursuit likely to be worth my while, or am I better off just letting it go and focusing on finding new tenants?

Joel Fine