In his City of God, Saint Augustine makes several observations concerning the Davidic Covenant and David's son King Solomon. You can find it in Book 17 of the City of God.
Augustine writes that Solomon erred greatly and could not possibly have fulfilled the Davidic Covenant. Augustine said that God allowed this inHis wisdom so that prideful Jews would be unable to claim Solomon as the true Davidic heir. Solomon filled his house with strange women and strange gods and his practices eventually led to the schism within Israel. Solomon in these ways is a kind of "anti-christ". As a king, he does appear to be like Christ, but at the same time his actions are contrary to the image of Christ (I don't mean to say that Solomon is an Antichrist is the traditional meaning of the word, by the way.)
This is why in Matthew 12:42, Christ says that he is the "greater than Solomon".