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Dear Mr. Schuh,
Thank you for posting your request on History Hub!
We conducted a search of the National Archives Catalog and located three file units regarding the Battle of Esperance. For access to and/or copies of these records, please contact the National Archives unit that has custody of it/them, as indicated in the catalog.
We also located on the Naval History and Heritage Command website an article titled Combat Narratives - Solomon Islands Campaign Part IV: Battle of Cape Esperance, 11 October 1942 that may be useful.
We hope this information is helpful. Best of luck with your research!