The presence of a runny nose has me suspicious that he might have a little upper respiratory infection going on. These usually are mild and don't require intervention with antibiotics unless the pet gets really congested and dumpy. Then antibiotics can help with a secondary bacterial infection, since a majority of these just start out as viral infections.

I can't give you a true diagnosis on the slobbering while laying down and resting. If he was having odor in his mouth or discomfort eating - then I'd be suspicious of oral lesions such as tooth injuries, ulcers, or severe gingivitis. If it was happening on and off while he was awake - I'd be suspicious of him eating something that greatly irritated his oral cavity.

Since it is happening as he is resting and sleeping - could he just have poor closure of his mouth and the normal salivary production leak? That is a possibility. Almost like a person drooling as they sleep.

I honestly am curious to know if there is anything in the mouth that could also be going on - even though it again doesn't sound like it. To rule oral lesions out, I would take him to the vet for them to further evaluate his mouth, teeth, gums, and back of the oral cavity. If nothing is found, that would be good. Then it might again be behavioral.

Hope all goes well,
Dr. Bruce