Hamlet's character is a very complex one and many would say that he does, indeed, display characteristics of the Oedipus complex, when Hamlet is analyzed from within the critical framework of psychoanalytic literary criticism. Bear in mind, though, that many literary analysts disagree with applying Freudian psychoanalytical principles to literature written before Freud's psycho-sexual theories were developed and known of.
From Hamlet's first appearance and his soliloquy in Act 1.2, Hamlet laments the marriage of his mother to his uncle. He tells us in his soliloquy in this scene that he's upset because his mother remarried so soon after his father's death and that she married her husband's brother. We can understand this when we know that, in the eyes of the Church, a woman married a man's family as well as the individual, therefore, Claudius was her brother in that sense, hence the reference to "incestuous sheets."
Even Gertrude recognizes at least some of the source of Hamlet's unhappiness, when in Act 2.2, she says she has no doubt the source is her "o'er hasty marriage." In Act 3, sc. 4, when Hamlet confronts Gertrude in her chamber after the play, the emotion he's been bottling up explodes.
Hamlet rants at this mother for her marriage to Claudius. He questions how could she stand to let him touch her. He asks her what she sees in Claudius. This exchange seems to show Hamlet just a little too emotional over his his mother simply remarrying unless we remember that their religion damns her to eternal hell for marrying her husband's brother; this would quite reasonably incense Hamlet.
Some read into this scene the psycho-sexual lustful love of a youth for his mother, but there is nothing textually definitive to the words spoken by Hamlet; a psychoanalytic interpretation depends solely upon the literary theory approach applied. Consider also the fact that he has discovered that his father's ghost correctly told him his uncle killed his father and the fact that he has just killed Polonius, and it is seen that it is normal that he would be emotional.
I think it makes some sense. first, he starts to doubt about the worth of life and Ophelia’s love that is indeed pure and deep, his mother’s remarry made him cast the whole world into the shadow. It really makes people feel strange how his mother could display such a big impact on him.second , hamlet is a thinker rather than a single minded revenger, he is always hesitated on action, but in his mother’s chamber, In Act 3, sc. 4, he just killed Polonius without thinking, and the single minded blood action is just against his characteristic. In a word, his unusual behavior towards his mother shows, to some degree, the Oedipus complex in him.
I don't think so because hamlet was not a protagonist character all tragedy began by the murder and we must not forget murder was done by Claudius and he had not said to Claudius to murder his father which shows that there were not even a single element of Oedipus complexity in hamlet.
Hamlet in a way is like Oedipus since he shares some qualities of a tragic hero. Oedipus is the tragic hero renown throughout time, and he himself led to his downfall as his Hamlet. The difference being, while Hamlet takes ages to act upon his actions and fakes madness in order to unveil the truth, he becomes mad himself. He struggles with the inward conflict he has within himself which leads to him spiraling out of control.