Database upgrade issues in SharePoint 2013

You have to read this blog before migration from SharePoint 2010 to SharePoint 2013 otherwise you will get error regrading with access issue or user not found in SharePoint or SharePoint sites or AD.

Troubleshoot database upgrade issues in SharePoint 2013

https://technet.microsoft.com/en-us/library/cc262967.aspx

Migrate from classic mode to Claims based authentication in SharePoint 2013,

https://technet.microsoft.com/en-us/library/gg251985.aspx