Since there are different views in different buddhist traditions there are certainly different meanings of 'to exist'. E.g. some see causality being the basis for existence whereas others say that causality reveals the assumption of existence to be baseless.
As a consequence there must be different connotations of 'to exist' involved because one meaning is compatible with causal dependence within the sphere of some minds while the other meaning is not so compatible with causal dependence in the sphere of some other minds.
your 'Per Buddhism' appears to be not specific enough.
In the context of everyday life ('Dharma in Everyday Life') it may be more relevant what intuitively/habitually happens in one's mind if one says or thinks 'This (or that) exists.' or 'This (or that) does not exists.' which is however only an instance of applying language and conceptuality. So this relevance in the context of everyday life is not restricted to 'to exist' but applies to all expressions of language.