The legal answer - highly unlikely, using a nuisance theory. The practical answer - it would be expensive and time consuming to fight it out and may last longer than the current tenants. There might be other avenues to correct the problem, such as Code Enforcement, but since you close to not tell us what the actual problem is it is hard to tell you what can be done.
Generally, the fact that a property is a "rental" and by some accounts may "devalue" surrounding properties is not actionable by itself. However the actions of the tenants may be actionable based on their own. There may be local code violations, violations of covenants or other violations. You've not indicated what the allegations are for the "devaluing" and what demands have been made. You will also have to address the "evidence" proving the tenants caused a devaluation and that the owner had a power to correct. In other words, in theory, yes there may be a cause of action with appropriate proof and evidence but it's far from easy and far from clear. Whether it is cost effective to pursue is another matter.
Disclosure: This answer and any information contained in this answer is not intended to be treated as legal... more
Disclosure: This answer and any information contained in this answer is not intended to be treated as legal advice. It is for informational purposes to educate about legal issues. You should contact an attorney for specific legal advice for your situation. Specific legal advice based on full knowledge of your specific situation and all facts may differ from general information. This posting does not create an attorney-client relationship or privilege of any kind. This attorney actively licensed only in the State of Georgia. If this is a Georgia matter, you may of course contact me to discuss possible representation.
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I've given written notice to my renters of the problem and set a time limit to solve the problem ( e.g. pick up rubbish, haul off old appliances) and tell them if I have to handle the problem, they will be billed.