I have a tenant who signed a 1 year lease back in Feb. Since that time, they have been nothing but problems for me, and my other tenants. They always pay on time, but the list of complaints against this from the other tenants is growing more and more each week. I have given them a few notices, but still they are becoming a problem. What would be my next step. I am in ohio. 

You definitely find yourself in a situation that no landlord wants to be in. What I can do is ask a few questions and provide my input. It is by no means exhaustive, and I am sure there are others who have better ideas, but here goes:

     With the notices, have you issued progressive notices? And by that I mean, was the second notice more stern than the first? Was the third written in such a way as to imply that the next notice will be one initiating the eviction process? 

     Do you have it structured so that your notices have ramifications? I.e., first notice is a courtesy; second notice is an X dollar fine; third notice is another X dollar fine and a final warning; fourth notice is the start of the eviction process.

Initiating the eviction process varies state by state, but maybe what they are doing does not rise to the level that the state deems eviction-worthy. In that case, the notices with attached fines would be the most you can do, but (and I don't know the applicable law off-hand here), you might not be able to start doling out fines if you didn't specify your notices would include them in the lease. You'd have to consult an attorney on that one. 

If your notices don't take a progression approach (each subsequent one becoming stricter), then you want to get on that. If your problem tenants continue to get notices, but the notices are essentially the same, then they're obviously not taking them seriously.

Another method I have heard of but have not had to implement myself yet is essentially paying them to move. You approach them, tell them that there are two options at this point. Option one is that you pay them, say, $400 for moving costs. You tell them that assuming they return the rental unit to rentable condition (top-to-bottom cleaning) that is to your satisfaction within a week, then they get their security deposit back along with $400 to help with moving costs. You agree to break the lease without court action, so long as you don't have to do any work yourself on the unit before renting it to someone else. Then you tell them that option two is that you take the numerous notices and neighbor complaints down the courthouse and file an eviction against them. You advise them that having an eviction on their record will severely inhibit their ability to get a decent apartment for years to come. Let them know that if you win, they will have to pay the court fees and will be liable to repay you the entirety of the lease. It will impact their credit. You can tell them that if they choose the eviction option that you will not provide a positive reference should a future landlord come calling.

Most people would likely choose the option where they make money to move. Some landlords scoff at this idea, but think about it: pay $400 to have them out in a week and have the unit in rentable condition and re-rented making money, or pay $1,200 +/- in court costs and have the tenant living there for a month or two, rent free. Then if you win the eviction, good luck having that tenant pay you anything back. Ever. If they go through an eviction, chances they care about their credit aren't big. And what do you think are the chances of an evicted tenant cleaning up the apartment you just kicked them out of?

I wish you the best of luck. Trouble tenants are a pain in the rear to deal with. There is that part of you that wants to work with them, that wants them to just be kind and respectful, but oftentimes, that is not going to happen. You must present yourself as an authority.