From The Pulitzer Prizes FAQ:
3. Must I be a U.S. citizen to apply for a Pulitzer Prize?
Only U.S. citizens are eligible to apply for the Prizes in Letters, Drama and Music (with the exception of the History category in Letters where the book must be a history of the United States but the author may be of any nationality). For the Journalism competition, entrants may be of any nationality but work must have appeared in a U.S. newspaper published at least once a week, on a newspaper’s Web site, on an online news organization’s Web site, and in some categories, in a U.S. magazine published at least weekly or its Web site.
. . . .
7. Are self-published books eligible?
Self-published books are eligible. Books must be published in hardcover or paperback form. We do not accept books that have only been published digitally.
Link to the rest at The Pulitzer Prizes