We shouldn't deny the 'existence' of these problems. [=we shouldn't deny that these problems are present or real]
long before the country had 'come into existence' [=begun to exist; come to have actual being]
I owe my very 'existence' [='life'] to their courage. [=I am alive because of their courage]
(..) He hears music in the sunrise. But he'd give it all up. He loves you that much. I don't understand. He can fall. He can give up his existence as he knows it. He can give up eternity and become... one of us. It's up to you. How do you know this? (..)1998 City of Angels