...is simply to declare; "See, that problem is solved. No one else could solve it because they were too stupid, or too weak, but I solved it because I'm smart and tough and they're not."

Anyone that points out the problem is NOT solved is dismissed as a fool, a coward, or evil. Trump simply doesn't care about the North Koreans missile threat, or the Iranian nuke threat, or the Russian cyber threat. All he cares is that his followers admire his strength, his intelligence, and his courage. Conversely, he is determined that his followers see his opponents as foolish, cowardly, or evil.

We've known this since the beginning, when he insisted his inauguration crowds were bigger than anyone elses.
Even though it didn't really matter, and no one cared, it was simply a fact about one of his claims (albeit a minor and insignificant one) that could be demonstrated to be false, so it was a threat to his legitimacy. He fears his legitimacy can be questioned because he was elected by a minority of voters, and he has always questioned the legitimacy of his enemies with insults, derogatory nicknames or outright lies. He must be aware (at least, I hope he is!) that most people see this, but he is not interested in "most people". He is interested in his base. He knows how religious cults work, and they do not require belief in the unbelievers, they only demand complete belief from the congregation.

None of this is particularly unusual or surprising. What I find terrifying is that about a quarter to a third of the American public falls for this. We don't just have a pathological President, we have a profoundly ignorant country.