I have researched the exact meaning of give up as in dictionaries.
But give up in the sentence below seems to have no object words, which means it is used as an intransitive phrasal verb.
We surveyed 500 smokers and found that over three quarters would like to give up.
And in the Macmillan dictionary as in the answer below which Mike added the link in, the intransitive version of give up means to stop doing something that you are trying hard to do, which seems to be inappropriate in this case. And also in Oxford dictionaries there are similar explanations regarding give up.
So I wonder if, also in this case, "give up" can mean quitting smoking.