Ajax features Ajax as a man who is determined to follow his will, no matter what, without the help of the gods. This is very dangerous.
Oedipus' determined thirst for knowledge, even when the truth is utterly horrible, is his most important character trait. Even when he blinds himself and is forced to live as a beggar, he still operates by sheer force of will in both Oedipus Rex and Oedipus at Colonus.
In Electra, the main character will not give up mourning her father until he's avenged, will not act like a woman and accept her place, and will not submit to her Aegisthus' and Clytemnestra's abuse. When she loses all hope of salvation (thinking Orestes is dead) and has been told of her parents plans to seal her in a cave to die, she decides to try and kill Aegisthus herself, in spite of being a woman.
In Man of la Mancha, Don Quixote's Determinator frame of mind is expressed in "The Impossible Dream":
This is my quest, to follow that star No matter how hopeless, no matter how far To fight for the right, without question or pause To be willing to march into Hell, for a Heavenly cause... And the world will be better for this: That one man, scorned and covered with scars, Still strove, with his last ounce of courage, To reach the unreachable star.
