You mean the "nothing at stake" difficulty ?   There's a solution to that in fact.  But it would alter so much the idea behind bitcoin, that it wouldn't be bitcoin any more.   The only difficulty with "nothing at stake" is the silly idea that consensus needs to be rewarded.  If you do proof of stake without reward, then there's no "nothing at stake" problem, because there's also nothing to gain from double-staking.  The problem in bitcoin and most alt coins, is that one wants to reward consensus, which makes consensus part of a gain strategy, which renders consensus decisions, exactly, part of a game-theoretical notion.

This is not necessary.  The only thing that was needed in the consensus decision, is to avoid Sybil attacks, to make your "evil" consensus decisions more probable and sustainable than would be the case if most users wanted the system to function honestly.   With proof of work, you have to waste economic resources to prove your 'unicity'.  Of course, nobody is going to waste huge amounts of resources from his pocket to help the system coming to consensus, so this is why PoW NEEDS to reward consensus decisions, which, in its turn, leads to all the game-theoretical problems, that end up by economies of scale, to centralize the consensus decision in the hands of an oligarchy. Which is what happened to bitcoin.
Without proof of work, there's no resources to be wasted ON PURPOSE.  But we need another way to protect against Sybil attacks, and to avoid that an evil minority pretends to be a large majority "voting over consensus".  One way would be to use "real world ID" or something, but that goes against the spirit of crypto.  But a very simple way is to "prove stake".  To associate your ID and your weight by stake.  You cannot Sybil it because you cannot prove more stake than you really hold.

The silly thing in proof of stake coins, is that they KEPT the reward scheme of PoW consensus. Let us not forget that the reward in PoW was necessary to compensate the economic losses of proof of work, that nobody would be willing to pay for otherwise, "for the community".  But in PoS, there's only a node you need to keep running.  All non-mining full nodes are voluntary contributions to the bitcoin network that do not get paid.  If these nodes were signing with PoS, they would establish a consensus decision, and there's no need for rewards.  

In fact, rewards, which are necessary in PoW, render indeed, PoS problematic with the "nothing at stake" strategy.  But without rewards, there is no "nothing at stake" strategy to be had, and the problem doesn't exist.

In non-rewarded PoS, the (only) reason to stake, is that you want the chain to work correctly, because you have value on it (your stake).  You have no incentive (because no reward) to keep on double-staking, because the only thing you do, is to increase the chances that your crypto fails, and the only thing you have, is a stake.