How did the Beatles' music influence modern literature?
I think that there would have to be a bit more of a limiting function in the nature of the question. The scope of "modern literature" is fairly broad. I will say that some of the thematic elements of modern literature's favorite targets were illuminated through music from The Beatles. Most of this will be found in the second phase of their music. Their exploration of themes such as alienation ("She Said, She Said" or "Nowhere Man") are excellent starting points for works of modern fiction where the investigation into notions of self identity often surround such an item. Consider most young adult fiction as a point of convergence here. The element of transformation found in songs like "Revolution" or "Helter Skelter" is something that strikes at modern literature's desire to present what is into what can be.
From an intellectual point of view, the music of The Beatles corresponds quite well to postmodernism, and the emphasis on deconstruction. One can see this in the closing songs of the last Beatles' album, "Abbey Road." The conclusion of "In the end, the love you take is equal to the love you make," is highly postmodern in its quality of deconstructing that which is accepted and forcing reexamination. Similar tendencies to favor deconstruction and a movement away from accepted rationalist approaches to being in the world can be seen in songs like "Let it Be" or "Obladi, Oblada." In these songs, modern intellectual literature in terms of philosophical elements become heavily influenced and channeled in the music of the Fab Four.