Jason教英文大口訣：姐懶趴短：give up 和give up on的差別
To give up on = to abandon; to cease to consider.
To give up = to quit (a habit or habitual practice); to surrender.
口訣： give up : give up on / 戒除讓步：拋棄斷念(姐懶趴短) XD
if it has a preposition, the meaning changes, you're absolutely right.
I give up (on myself) means I'm spent, I've had enough.
I give up myself means you're giving yourself to someone, as in submission.
I suppose the meaning changes, in regards to people, because if you give someone, you're handing them over so to speak. In my eyes, I see handing over someone to the police if it's "I gave up Bobby".
I'm really interested to hear what others say.
I think you're rightwhen talking about people. I think give up on myself or give up on someone else means to lose faith in or no longer rely on that person, and give up myself means to surrender to someone.
I think it's different when not talking about people though. I think 'give up on' implies that it is a decision made in exasperation. That you have been trying something, but it hasn't worked so now you're not going to bother anymore. 'Give up' implies more of a sacrifice or an effort, for example to give up smoking or chocolate. To give up you make an effort to stop doing something, whereas to give up on you no longer feel what you were doing is worth the effort you have put in. I don't think you'd really say 'I'm going to give up on chocolate' unless you were saying "I'm going to stop trying to use chocolate to make me feel better when I'm down, it doesn't work".!