您的疑問主要祥看give sb.up和give up sb./ sth.的區(qū)別
give up
e.g.I give up; tell me the end of the story.
give up sth.= give sth.up
e.g.The doctor told him to give up alcohol.
give up doing sth.
e.g.I've give up eating meat.
give sb.up
1、斷絕與...交往 e.g.She gave up a lot of her friends when she got married.
2、把某人交給警方,自守（to...）e.g.The murderer gave himself up (to the police).
give up on sb./sth.對…表示絕望；對…不抱希望
e.g.They refused to give up on their hopes.他們拒絕放棄自己的希望.
e.g.We are not that far apart to give up on the process.
我們之間的分歧,沒有大到放棄這一進程的程度.