Grammatical explanation for the different use of ‘continue’ and ‘continues’

My Vietnamese friend was signing a wedding card and wrote, “I hope your love continue to grow”. I pointed out that she should have said ”continues to grow”. She replied that someone else wrote, “May your love continue to grow”. I replied that this was correct but couldn’t explain why one expression used ‘continue’ and anther ‘continues’.

What is the grammatical explanation for the different use of ‘continue’ and ‘continues’ in the following two expressions:

• I hope your love continues to grow.
• May your love continue to grow.

The explanation, I'm afraid, is that may and hope are different words, and have different syntactic requirements.

There is some generality here: may is a modal auxiliary, like can, should, will, and these are always followed by the base form of the verb.

But it is not predictable from its meaning that hope takes as its object a tensed clause, optionally introduced by that. (It can also take a non-finite to clause). This is part of the "dictionary entry" for hope, and needs to be learnt along with its spelling and pronunciation. Expect (with similar though not identical meaning) takes the same kinds of object, but anticipate (again similar in meaning) can also take an -ing clause, but not a to clause).