I have seen numerous allegations from numerous people on social media stating that President Trump is a rapist, child rapist and pedophile, without one piece of verified or unverified evidence. Can President Trump sue for libel or defamation?
A person isn't required to state their evidence that the claim is true when they make the claim, and as a public figure, a defamation suit filed by Trump would be judged under the stronger "actual malice" claim, meaning that the statement was made with knowledge that the claim is false or with reckless disregard of whether it was false. You would have to look at the specific statement. It is generally not defamatory to hurl insults like "rapist!", "pedophile!", "criminal!" etc. against a public figure especially a political figure, since such word don't generally amount to an actual accusation of wrong-doing. On the other hand, a detailed but false claim purporting to relate factual events could cross the threshold. Hyperbole is not actionable.