Éowyn

In the original novel and Jackson's adaptation, it is implied that Saruman promised her to Gríma as payment for his services as a spy. In one scene, while mourning for her dead cousin, she is subjected to Gríma's obnoxious affections, which she spurns. She sings the dirge at Théodred's funeral. In the extended edition of The Two Towers, Éowyn is shown discovering, to her astonishment, that Aragorn is a long-lived Dúnadan. In the original theatrical release of The Lord of the Rings: The Return of the King, Éowyn plays a much larger role in the Battle of Pelennor Fields than in the book, where the only fighting mentioned is her conflict with the Witch-king and also Gothmog. Her speech revealing her identity is cut, replaced with the simple declaration ``I am no man!'' She also replaces Merry as the person to sit with Théoden as he dies. In the Extended Edition of the film, Éowyn is portrayed as being near death following her fight with the Witch-King; her brother finds her and screams in anguish because he fears that she is dead. She is later seen being healed by Aragorn, and meeting Faramir in the Houses of Healing.

Question: does eowyn die in return of the king
Answer: no