How can Freud’s concept of Oedipus complex be used to describe John the Savage?

Freud's Oedipus complex states that young boys unconsciously want to kill their fathers so they can have their mothers to themselves. Young boys want to have sex with their mothers, according to Freud. This leads them to experience a good deal of unconscious guilt.
John is unlike the other people in the World State because he was raised by his mother, Linda, on the Indian Reservation. He has a troubled relationship with his mother.
In his earliest memory, he has her all to himself in bed:

It was very hot. They had eaten a lot of tortillas and sweet corn. Linda said, “Come and lie down, Baby.” They lay down together in the big bed. “Sing,” and Linda sang. Sang “Streptocock-Gee to Banbury-T” and “Bye Baby Banting, soon you’ll need decanting.”

But soon, although his father is not on the scene, he has to compete for her attention with other men who also want her sexually—and he loses her to them, just as a young boy loses his mother to his father:

There was a loud noise, and he woke with a start. A man [Popé] was saying something to Linda, and Linda was laughing. She had pulled the blanket up to her chin, but the man pulled it down again.

John is banished so that Popé can have sex with his mother. Popé's phallic masculinity is symbolized by his hair:

His hair was like two black ropes

We are told John hates Popé and the other men who visit his mother:

He hated Popé. He hated them all—all the men who came to see Linda.

When he discovers Shakespeare, John is immediately drawn to Hamlet, a text Freud pointed to as playing out a repressed version of the Oedipal conflict. John especially focuses on Hamlet's Oedipal relationship with his mother. John instantly perceives Linda in Hamlet's accusations about his own mother:

In the rank sweat of an enseamed bed,
Stew’d in corruption, honeying and making love
Over the nasty sty.

Both John and Hamlet want to make love to their mothers and both are jealous and filled with guilt over their unconscious desires. In the Freudian reading of the play, Hamlet wants to kill his uncle Claudius not because Claudius killed his father, but because Claudius is doing what Hamlet secretly wishes he could do: sleeping with his mother.
In John's case, after seeing Pope in bed with his hand on his mother's breast and his braid draped across her throat, the jealous John tries, unsuccessfully to kill his rival by stabbing him.
We can see John's desire to be whipped as a way to alleviate his unconscious guilt, just as we can see his self-flagellation after he moves to the World State as yet another manifestation of his intense guilt.
Lenina, the woman John falls in love with in the World State, is very much like his mother, and therefore represents another facet of his Oedipal desire. Because of his very confused relationship with his mother, who is both loving and rejecting towards him, John lashes out at Lenina. He becomes very frightened when Lenina unzips and steps out of her unitard suit and approaches him sexually: he both desires her and yet has to guard against the desire as he had to guard against his desire for his mother. He projects the anger he felt towards his mother for sleeping with other men against Lenina, calling her a whore and a strumpet:

The Savage caught her [Lenina] by the wrists, tore her hands from his shoulders, thrust her roughly away at arm’s length.
“Ow, you’re hurting me, you’re. oh!” She was suddenly silent. Terror had made her forget the pain. Opening her eyes, she had seen his face-no, not his face, a ferocious stranger’s, pale, distorted, twitching with some insane, inexplicable fury. Aghast, “But what is it, John?” she whispered. He did not answer, but only stared into her face with those mad eyes. The hands that held her wrists were trembling. He breathed deeply and irregularly. Faint almost to imperceptibility, but appalling, she suddenly heard the gneding of his teeth. “What is it?” she almost screamed.
And as though awakened by her cry he caught her by the shoulders and shook her. “Whore!” he shouted “Whore! Impudent strumpet!”

While Huxley critiques the sterility and lack of deep relationship in the World State, he also shows what an Oedipal mess families can be.