Recently our SQL server harddisk is almost full. I cannot perform any update action in SharePoint. So I remote in the SharePoint server and use PowerShell to delete some site collection and then their corresponding content databases. The content database is disappeared in the CA and I thought it is good.

However, our DBA told me the database still exist in SQL server in single user mode. I guess the deletion have only processed in half due to the insufficient harddisk.

Also, below log keep coming up at SQL server: Login failed for user 'DOMAIN\FarmAdmin'. Reason: Failed to open the explicitly specified database.

The SQL server harddisk is in good siutation now but the log keep coming. What should I do?

If you run:

Get-SPDatabase | Select Name,Server

Does the database in single user mode/the error you're seeing in SharePoint still appear?

Trevor, no I don't see the DBs in single user mode and in normal mode (DBA turned it back to normal mode manually)

After we rebooted all the servers the error log have reduced a lot. So I have to let it be.