outside the field of mathematics, is it possible to prove that something doesn't exist ?

a bit like going into a darkened room looking for a black cat that you're not even sure is there - at what stage can you feel confident that the cat isn't there ?

an analogue case in astronomy was the case of the planet Vulcan, which was supposed to orbit the sun inside the orbit of mercury in order to explain irregularities in the latter's rotation

sightings were made from time to time but never confirmed, and in the end, with improvements in telescopes and search methods, the size of a body that could possibly reside in an intra-mercury orbit until shrank until it approached a size below which the body could no longer be described as a planet

as soon as the boundary conditions for the existence of such a body did no longer intersect with the boundary conditions of the definition of a planet, the case for the existence of Vulcan could be said to be disproven

in view of the above i'd have to give a qualified yes in answer to the question, but i'm not very confident that the methodology can be extended to a wider range of proofs of non-existence - the example may only highlight the possibility of proving the non-existence of a well-defined object in a confined space