Judah is only incidentally mentioned to form a contrast to Israel.
by the Lord their God - more emphatic than “by Myself”; by that Jehovah (Me) whom they worship as their God, whereas ye despise Him.
not ... by bow - on which ye Israelites rely (Hos 1:5, “the bow of Israel”); Jeroboam II was famous as a warrior (2Ki 14:25). Yet it was not by their warlike power Jehovah would save Judah (1Sa 17:47; Psa 20:7). The deliverance of Jerusalem from Sennacherib (2Ki 19:35), and the restoration from Babylon, are herein predicted.