From a dissertation:

James Joyce and His Influences:
William Faulkner and Anthony Burgess
An abstract of a Dissertation by
Maxine Burke
July, 1981
Drake University

https://escholarshare.drake.edu/bitstream/handle/2092/986/Untitled.pdf?sequence=1&isAllowed=y

CONCLUSION
To summarize James Joyce's influence on Burgess and Faulkner is to say that, on the whole, his influence is mostly in his way of telling a story and in his
use of language.  In Chapter One many of the things that Joyce does
with language were discussed: changing word order, writing long passages without punctuation, combining words, and using slang and different dialects. In addition, Joyce uses associative thinking--any idea is seen in association with other things--and there is no end to associations. (The latter is an important
aspect of his stream-of-consciousness method.) He uses obscure words, words of the past out of old dictionaries, and, also, he uses the same word (or the same
word sound) in different contexts to create whole new meanings. And finally, he constructs new words--especially in Finnegans Wake--that present a challenge to the reader.
Because Joyce's linguistic innovations have so much to do with the way he structures his stream-of-consciousness passages and descriptions of the char
acters and their emotions, this technique is perfected to the greatest degree. With his use of mythology, the author intends, in both Ulysses and Finnegans Wake, to present universal history. His parallels in Ulysses with those of Homer's Odyssey are meant to show that time and space are suspended. Joyce's Ulysses, as well as his other works, is about human nature; and Ulysses, as well as his other stories, ends on an optimistic note. (Joyce's Dubliners, of course, is quite pessimistic until the last story, "The Dead," where his optimism becomes apparent as Gabriel attempts to set aside his isolation, to have empathy for others and to attain "the full glory of some passion)
In Chapter Two, then, it was shown how the travel motif and the wasteland theme in Ulysses differ from that of William Faulkner's Mosquitoes. In Ulysses the travel motif ends on a positive note (Leopold coming home to rest by the side of his Molly); and the wasteland theme changes into a fruitful one (when Mrs. Purefoy's baby is born, and the rain begins). On the other hand, the journey in Mosquitoes is a failure (the characters leaving the yacht feeling, to various degrees, indifference, frustration, and anger); and the wasteland theme remains (as the story ends on a grim James Joyce, "The Dead," The Portable James
Joyce, ed. Harry Levin (New York: The Viking Press,
1965), p. 241.note--with a decadent fantasy). And that the as two pages
of the novel find the tiresome Talliaferro still talking about seducing a girl. However, lIse Dusoir Lind in an article, The Effect of Painting on Faulkner's
Poetic Form, believes, unlike this writer, that as the decadent theme evolves--expressed through the heat of the city which causes decay--the idea is there "that
new life, new art, comes out of rottenness and death.,,

 Faulkner's "The Bearll was also discussed.
The influence of Joyce on Faulkner is shown through language, time and timelessness, the journey motif, and the stream-of-consciousness technique.
Joyce's way of telling a story has its similarity and parallel in Burgess' story of Shakespeare's love life, Nothing Like the Sun, as Burgess follows Stephen's
(Joyce's) discussion of Shakespeare in Ulysses. Burgess in his work, Urgent Copy, a book of his literary criticism and in his Shakespeare, which is about the
life and society of Shakespeare, supports the main points he makes about the life of WS in Nothing Like the Sun, those same points that Joyce's Stephen Dedalus
has theorized about to the literary group assembled in lIse Dusoir Lind "The Effect of Painting on Faulkner's Poetic Form,,,'Faulkner, Modernism, and Film
ed. Evans Harrington and Ann J. Abadie (Jackson: University Press of Mississippi, 1979), p. 135. the library. Thus in Chapter Three the similarity of
the two stories, about Shakespeare, was traced.  

In sum, Joyce's Ulysses has provided the basis for examining and analyzing his influence on William Faulkner's "The Bear" and Mosquitoes and Anthony Bur
gess' Nothing Like the Sun. That the pattern of Joyce's influence on the twentieth-century novel is evident, critics agree. Adams praises him: "The positive influence of Joyce has proved wide, deep, and enduring. Steinberg asks, "Why Joyce? And why at that particular time?" And he concludes that "the
answer must be: because he was Joyce." These are
fitting comments for a great writer.