不要放弃自己英文

Don't abandon me. 这个倾向于抛弃，遗弃Don't give up on me.这个是放弃不管的意思楼主看语境使用吧，呵呵

Though others don't believe you, never give up yourself!

应该是don‘t give up yourselfgive up on v. 对...不再抱有希望eg We had to give it up as a bad job. 我们只得对此不再抱有希望。 give up 放弃

You shouldn't give up yourself even if the others didn't trust you.

别放弃我Don't give up on me!

please do not give up me！！because i care about you very munch！

So this life has given everyone a present 生活给我们每人一件礼物 beautiful shiny and new 漂亮闪光 everyone but you 每个人都有，除了你 golden ribbons ,diamonds 金黄色的缎带，钻石 line everyone's path that leads to wide open doors 每个人总有一条合适的宽广的道路（世界） everyone's but you 只有我没有 wide open doors 宽广的世界 hold on, keep on 坚持住，坚持住 even when the road seems very long 即使这条艰难的跟看起来很漫长 open you eyes 张开你的眼睛 even if it's cold now 即使它此刻十分的寒冷 there's one thing you should know 有一件事，你需要明白 rain will turn into snow 总有一天，雨滴终究会变成雪花 all the rain turns to sonw 所有的雨滴都将会变成雪花