Éomer

Éomer has a major role in the Battle of the Pelennor Fields, the pivotal battle of The Return of the King. After fighting bravely for Rohan and Gondor, he is dismayed to find Théoden mortally wounded in the battle. Théoden appoints him King of Rohan with his dying breath. Then, seeing an unconscious Éowyn seemingly dead on the battlefield, Éomer decides to throw himself and the remaining Rohirrim at the enemy, all the while cries of ``Death!'' have replaced the traditional songs of slaying with which the Rohirrim had initially entered the battle. Aragorn saves them when he arrives unexpectedly from Pelargir, fulfilling his prediction that they would fight together again. Aragorn's arrival and reinforcements provoke a rout among the Orcs, and he and Éomer win the battle. Aragorn's healing hands later restore Éowyn to perfect health.

Question: does eomer die in lord of the rings
Answer: no