'there might exist' is correct and can be used in written English.
It can be used to express the possibility that something exists or is true. For example: "There might exist a way to bridge the gap between the two sides".
"Valéry expressed the hope that one day there might exist A Unified History of the Things of the Spirit, which would replace every history of philosophy, art, literature and the sciences," Calasso discloses.
"Antitrust law is now, and I think quite appropriately, focused on identifying where there might exist a particular competition problem in the sense of the creation of economic power in certain markets.
Perhaps in the sharpened interstices of the "m" or the slightly more pinched ellipse of the "o" there might exist a statement of what the Modern wants to be -- you just have to squint to see it.
Whatever it was, I'd started to think there might exist some suffering people who had not brought it upon themselves, and who might therefore be worthy of some help, some help from us, the larger group.
As LCL circuit is used in the hub, there might exist prolonged oscillations in the hub.
Therefore, there might exist two kinds of redundancy in the network.
Experimental results indicate that there might exist a FM coupling between Mn3+ and Cr3+.
Therefore, there might exist an optimum point between the two extreme cases.
Since there might exist more than one disparity sharing the same minimum cost for some cases.
However, since the sample size is quite small, there might exist systematic bias.
Previous research indicates that there might exist a link between the experience of pain and mental distress.
