1、意思上的区别
give up：放弃；投降；把…让给；戒除。
give up on：不再相信，不再信任。
2、用法上的区别
give up通常只是一般性地表示将某物让给、交给或献给他人或用作他用。
give up on sb表示的是对…表示绝望；对…不抱希望。
例句:
①、give up
After a fruitless morning sitting at his desk he had given up.
他在书桌前徒劳地坐了一上午之后便放弃了。
She gave up her job to join her husband's campaign
她辞去工作，加入到丈夫的宣传活动中。
②、give up on
He urged them not to give up on peace efforts
他力劝他们不要放弃对和平的努力。
My teachers gave up on me.
老师们对我不抱任何希望了。
Never, ever, give up on yourself.
任何时候都不要自弃。
扩展资料
同义词解析：
abandon
vt.放弃，抛弃;离弃，丢弃；使屈从；停止进行，终止。
n.放任，放纵；完全屈从于压制。
He claimed that his parents had abandoned him
他声称父母遗弃了他。
The authorities have abandoned any attempt to distribute food
当局中止了分发食物的尝试。
Logic had prevailed and he had abandoned the idea.
最终理智占了上风，他打消了那个念头。
