Raising verbs
(1) There seems to be a problem.
(2) There is a problem.
(3) We didn’t expect there to be a problem.
If this is correct, then there in (1) has raised from subject position in the embedded clause to subject position in the main clause, as shown in (4) below (where the strikethrough font shows the initial merge site for there):(4) There seems there to be a problem.
Extending this analysis to sentences such as John seems happy, we have the following:
(5) John seems John happy.