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Discover LudwigSuggestions(1)
The phrase "and have existed" is correct and usable in written English.
It can be used to indicate the ongoing state of existence of something from a past point to the present.
Example: "These species have adapted to their environment and have existed for millions of years."
Alternatives: "and continue to exist" or "and have been present".
Exact(21)
Intellectuals do exist in this country and have existed.
Complementary are already available to public consumption and have existed often for hundred's of years.
The pattern may well be real — and have existed for decades.
"These are all problems that are well known and have existed for years.
"The five countries are all cradles of civilisation and have existed in peace for thousands of years," he said.
In areas where scrublands occur naturally, especially as a result of nutrient-poor soils, and have existed for a long period, plant diversity can be astonishingly high.
Similar(39)
BTW, clean coal technology exists (and has existed for years).
This impulse exists and has existed among waiters, physicians, coachmen, artists, prostitutes, dishonest officials, soldiers, nobles, crusaders, gamblers, and beggars.
The problem is that Thatcherism still exists and has existed ever since she walked out of Downing Street," he says.
It was one of the first canonaries and has existed there in some shape or form for eight centuries.
The perceptions of the learning culture in the organisation of teachers' work are high and has existed and practised by teachers in their organisation.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com