The problem in Oedipus Rex is the king's refusal to accept the truth which Teiresias brings him: Oedipus himself is the cause of the plague because he is the murderer of the previous king of Thebes,
When the plague besets Thebes, the people approach their king, who has been made king because previously he so wisely solved the mystery of the sphinx. They beg him to save them from the plague that beseiges them, so Oedipus speaks with his brother-in-law, Kreon. From him Oedipus is told that
The god commands us to expel from the land of Thebes
An old defilement we are sheltering (99-100).
When pressed, Kreon expands on the message, explaining that it was "Murder that brought the plague-wind in the city" (105) and Apollo has commanded that Thebes rid itself of this murderer. Specifically, it is the man who murdered the former king of Thebes, who was King Laius.
While Oedipus acknowledges this message, he fails to accept the truth that Teiresias later reveals only under duress; that is, Oedipus himself is this murderer. Oedipus rejects this truth and, in his hubris, he defies the words of the Oracle of Apollo.
However, after he angrily banishes Kreon from Thebes, his wife Jocasta, who is so distraught over the enmity between her brother and her husband, tries to help Oedipus solve the mystery of the plague by telling him that an oracle told King Laius, her husband, that he would be killed by his own child. As Oedipus learns that the location of the murder of Laius was at the point where three roads meet in Phocis, he realizes that this location was where he once killed a man of position. And, he begins to suspect that he is, in fact, the murderer. When he finally accepts his guilt, the problem is solved, although tragically.