There are three dominant sources for academically sound literary analysis essays. The first is collections of critical essays such as are found in your school or university library in the Reference section. An example of this would be The Columbia Companion to the Twentieth-Century American Short Story or Nineteenth-Century Literature Criticism. A variation of this is collections of book reviews such as in Book Review Digest; New York Times Book Review also provides quality book reviews by experts in literature.
The second is books published by literary critics that cover the topic you are interested in. These also would be available from your academic library. An example would be Victorian Women: A Documentary Account of Women's Lives in Nineteenth-Century England, France, and the United States by Erna O. Hellerstein, Leslie P. Hume. Many published criticism books are also available for purchase.
The third source is scholarly journals. These periodicals are listed in guides like Ulrich's Periodical Directory. An example of such a scholarly journal listed in a periodical guide is Modern Fiction Studies. A well know scholarly journal in literature is the Oxford Literary Review, published, ironically, by Edinburgh University Press (as opposed to Oxford University Press).
Three well known and much used reliable review and critical essay sources are Magill, Gale and Salem Press. These are available through eNotes resources on a vast number of titles including "A Rose for Emily" by William Faulkner (see "Critical Evaluation" and "In-Depth"). As a final comment, many critics make their work available online, for instance, Jim Barloon, The University of St. Thomas has a critical article available through Southeast Missouri State University's "Centre For Faulkner Studies" and LiteraryHistory.com offers a wide range of Literary Criticism on the Internet. (Look for .edu or .org endings to the URL address.)
Critical Sources, Shorter University