So, we have checked both your Sites. The only difference between both Sites was the usage of the “Relevanssi” plugin. On your .dk domain Site, there wasn’t any Relevanssi plugin used but on your .se domain Site, the Plugin was being used there which we deactivated and then the Search was working fine.
So, it was the Plugin end issue in this regard on your .se Site.
Please check back your Site after completely clearing the browser and server cache.