Balancing between students who do homework and those who do not
If 40% of the students aren't doing their homework, and you rely upon students doing homework for your pedagogy style to work, then something is seriously wrong.

You have two options:

(1) Make homework dramatically more appealing.


Put much more effort into the homework--make it fun!  E.g. calculate strain on an iPhone screen instead of a aluminum sheet; don't have someone read a novel but rather ask key questions about it such as to list all the times some character/historical figure expressed defiance against the state.
Institute quizzes that are drawn directly from the homework.  Do them practically every day.  Staring at a blank sheet of paper and not knowing what to do is a lot more uncomfortable than hearing you babble about something incomprehensible.
Change the grading scheme so homework is most of the grade (if you're allowed).


(2) Make homework dramatically less necessary.  (Note: usually not an option for mathematics.)


Do the key problems on the board in class instead of assigning them as homework.  (Assign a similar problem as homework, possibly after you've done it in class.)  Not possible for literature review, of course.
Rely upon in-class participation instead (if you have the personality to make it work, and the homework is of the right type).
Don't make the learning environment one which requires the students to do the homework in order to understand most of the next lecture.  Lecture on the important points, review at the end of one lecture and the beginning of the next, and go on.  They might not develop their skills at doing problems, but at least they'll have some hope of following for a while.  Probably won't work with literature, but almost everything else can be quite successful.