Albert Barnes Commentary 1 Kings 15:4

"Nevertheless for David`s sake did Jehovah his God give him a lamp in Jerusalem, to set up his son after him, and to establish Jerusalem;" — 1 Kings 15:4 (ASV)

To set up his son - The idolatry of Abijam deserved the same punishment as that of Jeroboam (1 Kings 14:10–14), Baasha (1 Kings 16:2–4), or Zimri (1 Kings 16:19): the cutting off of his seed and the transfer of the crown to another family. That these consequences did not follow in the kingdom of Judah was because of the faithfulness of David, which brought a blessing on his posterity.

Few things are more remarkable and more difficult to explain by human reasoning alone than the stability of the succession in Judah and its excessive instability in the sister kingdom. One family in Judah held the throne from first to last for nearly four centuries, while in Israel there were nine changes of dynasty within two hundred and fifty years.