Passages concerning the Son of Jesse
David was made King over Israel.
1-Kings (KJB) 8:
16 Since the day that I brought forth My people Israel out of Egypt, I chose no city from any tribe of Israel to build a house where My name might be praised, but I chose David to be over My people Israel.
An Eternal Throne
David had been promised that his seed would rule over Hebrews forever. This blessing was confirmed to Solomon.
1-Kings (KJB) 2:
45 But King Solomon shall be blessed, and the throne of David shall be established before the LORD forever.
God spoke to Solomon promising him an eternal lineal right to the Kingdom in the name of the promise given to David.
1-Kings (KJB) 9:
5 then I will establish the throne of your kingdom upon Israel forever, just as I promised to your father David, saying, 'You shall not fail to have a man upon the throne of Israel.'
1-Kings (KJB) 11:
36 To his son will I give one tribe, so that My servant David will always have a light before Me in Jerusalem, the city in which I have chosen to put My name.
In the Name of David
Solomon prayed to God on behalf of his kingdom in the name of his father David.
1-Kings (KJB) 8:
25 Therefore, LORD God of Israel, now keep what You promised Your servant David my father, saying, 'You will not fail to have a man sit before Me on the throne of Israel, so long as your sons take heed to their way, that they walk before Me as you have walked before Me.'
David was Chosen
When Solomon built the Temple he praised the Almighty and quoted the promise God had made regarding the lineage of David.
2-Chronicles (KJB) 6:
6 but I have chosen Jerusalem for My name to dwell there, and I have selected David to be over My people Israel.
David the Anointed
In Psalms David is referred to as the "Anointed," in Hebrew "Mashiach" i.e. Messiah.
50 He gives great deliverance to His king, and shows lovingkindness to His anointed, to David and to his descendants for evermore.
Psalm (KJB) 89:
20 I have found David, My servant; with My holy oil I have anointed him:
Temporary Rejection of the Son of Jesse!
When the Ten Tribes rebelled against Rehoboam the son of Solomon they described themselves as rejecting the son of Jesse, i.e. descendants of David. The Future Redemption will come when they repent and return to request that David (i.e. the Messiah, son of David) rule over them (Midrash Shmuel 13; Midrash Yalkut Shimeoni-2, remez 106; Rashi on Hosea 3:5).
1-Kings (KJB) 12:
16 So when all Israel saw that the king did not listen to them, the people responded to the king, saying, 'What portion do we have in David? We also do not have an inheritance in the son of Jesse. To your tents, O Israel, and see to your own house, David! So the people of Israel departed to their tents.
The Future Messiah will be a Branch of David
The Future Messiah is referred to as a Branch of David i.e. an offshoot meaning a descendant.
Jeremiah (KJB) 33:
15 In those days and at that time, I will cause a righteous Branch to spring up for David; and he shall execute justice and righteousness in the earth.
Ezekiel (KJB) 34:
24 I the LORD will be their God, and My servant David shall be prince among them. I the LORD have spoken.
Hosea (KJB) 3:
5 Afterward the children of Israel will return and seek the LORD their God and David their king. They will come in fear to the LORD and to His goodness in the latter days.
Ingathering the Exiles, The Stem of Jesse i.e. David.
Isaiah (KJ2000) 11:
1 And there shall come forth a rod out of the Stem of Jesse, and a Branch shall grow out of his Roots:
2 And the spirit of the LORD shall rest upon him, the spirit of wisdom and understanding, the spirit of counsel and might, the spirit of knowledge and of the fear of the LORD;
3 And his delight shall be in the fear of the LORD: and he shall not judge after the sight of his eyes, neither reprove after the hearing of his ears:
This "Rod out of the Stem of Jesse," and Branch Growing out of his Roots is the future Messiah son of David son of Jesse.
He will judge the Earth and reform mankind (Isaiah 11:4-9). He will also ingather the Exiles including those of Ephraim and the Lost Ten Tribes (Isaiah 11:11–13).
Jeremiah (NKJV) 33:
14 Behold, the days are coming, says the LORD, that I will perform that good thing which I have promised to the house of Israel and to the house of Judah:
15 In those days and at that time
I will cause to grow up to David
A Branch of righteousness;
He shall execute judgment and righteousness in the earth.
16 In those days Judah will be saved,
And Jerusalem will dwell safely.
And this is the name by which she will be called:
THE LORD OUR RIGHTEOUSNESS.
17 For thus says the LORD: David shall never lack a man to sit on the throne of the house of Israel;
18 nor shall the priests, the Levites, lack a man to offer burnt offerings before Me, to kindle grain offerings, and to sacrifice continually.
Jeremiah (ESV) 33:
19 The word of the LORD came to Jeremiah: 20 Thus says the LORD: If you can break my covenant with the day and my covenant with the night, so that day and night will not come at their appointed time, 21 then also my covenant with David my servant may be broken, so that he shall not have a son to reign on his throne, and my covenant with the Levitical priests my ministers. 22 As the host of heaven cannot be numbered and the sands of the sea cannot be measured, so I will multiply the offspring of David my servant, and the Levitical priests who minister to me.
Jeremiah (ESV) 33:
23 The word of the LORD came to Jeremiah: 24 Have you not observed that these people are saying, The LORD has rejected the two clans that he chose? Thus they have despised my people so that they are no longer a nation in their sight. 25 Thus says the LORD: If I have not established my covenant with day and night and the fixed order of heaven and earth, 26 then I will reject the offspring of Jacob and David my servant and will not choose one of his offspring to rule over the offspring of Abraham, Isaac, and Jacob. For I will restore their fortunes and will have mercy on them.