Issue:

Database is in compatibility range and upgrade is recommended

Solution:

Please find the below solution to upgrade the SharePoint DB.

  1. In SharePoint Central Admin, click BACKUP AND RESTORE. Then perform a FULL BACKUP.
  2. Start the SHAREPOINT 2013 MANAGEMENT SHELL (make sure you RUN AS ADMINISTRATOR).
  3. CD into C:\Program Files\Common Files\Microsoft shared\Web Server Extensions\15\BIN.
  4. Paste the following command and press Enter: PSConfig.exe -cmd upgrade -inplace b2b -force -cmd applicationcontent -install -cmd installfeatures
  5. This will take a few minutes to complete so just wait.
  6. Go back to your SharePoint Central Admin console and click MONITORING (left menu) > REVIEW PROBLEMS AND SOLUTIONS. If Databases Running in Compatibility Range, Upgrade Recommended still shows then click on it. Click the REANALYZE NOW button on the top.
  7. Hopefully, it only complains about your content database and Bdc_Service_DB.

How To upgrade your Content Database:

Paste the following into your SharePoint 2013 Management Shell Upgrade-SPContentDatabase and then enter the name of your content database at the Identity

(Get-SPDatabase | ?{$_.type -eq
“Microsoft.SharePoint.BusinessData.SharedService.BdcServiceDatabase”}).Provision()

Database is up to date but some sites are not completely upgraded: http://expertsharepoint.blogspot.de/2014/03/data-base-is-up-to-date-but-some-sites.html

See more

http://expertsharepoint.blogspot.de/2014/09/database-is-in-compatibility-range-and.html