Can I use passive form in this case? The problem is still exist.
Both of them are correct?

1,The problem is still exist.
2,The problem still exists.

If so, then what is the key difference?
I assume the first implies that this problem has a reason.

Question

Can I use  passive form in this case? The problem is still exist.
Both of them are correct?

1,The problem is still exist. 
2,The problem still exists.

If so, then what is the key difference? 
 I assume  the first implies that this problem has a reason.

Answer

I think the first one is not correct as for passive sentences you basically need a subject and an object. The object un the active sentence becomes the "patient subject" in the passive. Here you only have one of these two elements, so passive form is not possible. Keep the second sentence and forget the first one ;) It just does not make sense.
Apart from that, verb to be+another verb usually implies continuos tense.