To sleep on someone's sofa or floor because there is no bed spare.
To make heavy with sleepiness or imperfect sleep; to make dull or stupid.
To nod off; to fall asleep.
To be sleepy and inactive.
To advance drowsily. (Used especially in the phrase "drowse one's way" ⇒ sleepily make one's way.)
The state of being sleepy and inactive.