Elena

What is the current state of research about the existence David (and Salomon)?

Is there any archeological evidence? Is there any other source outside the bible?

semiopen

Israel Finkelstein thinks he existed, probably as a local war lord. Jerusalem at that time was only a few acres in size. He thinks he existed because the book of Samuel contains scenarios that existed in tenth century Judea but not later. In addition to which the Tel Dan Stele may refer to the house of David. Both those things together suggest his existence is reasonable if not entirely convincing.

Solomon is less clear (if that is possible). A guy on another forum suggests he may be an Judean interpretation of Hamurabi which I like despite the time difference.

It is pretty certain that there was no Judean kingdom before the Israel kingdom. From what I understand the first temple existed but was no big deal architecturally, maybe similar in dimensions etc. to various Caananite temples that have been excavated.

Doug Shaver

It's shaky, but at this point it's probably more reasonable to think David did exist than that he didn't. There is some meager evidence for his historicity and none against it.

Assuming he existed, he almost certainly had a successor, and the only documentation we have on the subject says he was succeeded by one of his sons and that the son's name was Solomon.

Semiopen already mentioned the Tel Dan stele. Nothing else outside the Bible confirms anything nontrivial about that period of Jewish history.