The alignment definitions for D&D 5e are somewhat vague, which was the case in previous editions as well. I think your first step is to find out just what they think it means to be evil. As evil characters, what are their goals? If they want to be able to rape, pillage, and murder their way across your game world, and you're wanting to tell stories about heroes who save the world, then that's going to be a problem.
I think a lot of times, though, players have a less grandiose idea of what it means to be evil. Maybe they want to be a jaunty group of smugglers and thieves, living on the outskirts of society, pitting their wits against law enforcement and the powers-that-be, but never failing to help out the little guy. In that case, they would be easy to motivate to saving the world. It could even be more interesting if they have to fight law-enforcement in order to save the world.
They might also just want to focus on amassing a great deal of power for themselves in whatever way is most expedient. In that case, you could show them that the easy path to doing that would be to save the world. There are side benefits to being a hero in the eyes of society, and looting isn't frowned on when you're doing it to the BBEG and his goons.
Or maybe they've been irritated in the past by DMs who wouldn't let them waterboard the goblin prisoner who knew where and when the captured prince was going to be sacrificed, and they're trying to free themselves from those kinds of moral dilemmas, so they can just "win" the game. In that case, you just need to reassure them that you're not going to throw trolley problems at them, and then punish them for making the "wrong" choice.
Once you understand why they want to run evil characters, and what to expect from them, then you can decide how, or whether, those characters will fit into the game you want to run.
I once ran a game for one of my nephews when he was around 13. He had read the Dragonlance books and wanted to run a Raistlin-type character--a wizard, who has a lust for power and seeks to attain it in any way he can. He actually named the character Rassalan.
This was back in second edition, when kits were the rage. He chose the Witch kit, because it would provide his character with a magic item at first level. In the kit, it said that the character acquires the item by making a deal with a fiend. I chose to have him roleplay the deal.
The item he wanted was a Dagger of Venom, and he got it from an imp who wanted him to use it to kill his mentor. He readily agreed. Then he returned to his home, and I roleplayed an interaction between him and his mentor. His mentor told him that Rassalan had learned all he could teach him, so he gave him 200gp and told him he should move to Waterdeep where he could learn more about the Art.
I made the guy so nice and personable, that my nephew decided he liked him too much to kill him. Basically, when it came to performing an act that really would have felt evil to him, he balked. That wasn't what he had in mind when he chose to play an evil character. He wanted the game to be about his character becoming insanely powerful, rather than running around helping little old ladies across the street (figuratively). He didn't think that he could get that kind of game playing a good character, so he chose the evil alignment. A better discussion beforehand might have revealed that.
To finish the story of his character, the imp showed up that night, and said, "What are you doing? We have a deal. Go kill him." Rassalan refused, so the imp demanded his dagger back. Makes sense, right? My nephew wanted that dagger too bad, though, so Rassalan refused to return it. A fight ensued, and a first level wizard was just no match for an imp, not even when armed with a Dagger of Venom. He was killed. The mentor woke up, though, and destroyed the imp. He had Rassalan raised from the dead, and paid for it by selling the dagger. :)