I searched through all of the online cemeteries but didn't find them. Not all of the indexed cemeteries are online.
1910 Yellowstone, Woods, OK
Gideon F. Campbell, b. IA, 37, marr 6 yrs, general farmer
Martha, wife, b. NE, 22
Acey, b. OK, 5
Laura, b. OK, 4
1920 Coal, Scott, Arkansas
Gideon Manhill Campbell, b. IA, 47, farmer
Martha, b. NE, 31
Asa, b. OK, 14
Laura, b. OK, 13
Stella, b. AR, 8
Jessee, son, b. AR, 4
Martha may Bales Campbell
Born: Aug 8, 1888
Death: Jan 26, 1962
Buried: Gipson Cemetery, Bates, Scott, AR along with Gedion.
Source: findagrave.com along w/ tombstone pic & other info
I couldn't find any of them in Arkansas Census records in 1930 and 1940.
Gideon Franklin "Manhill" Campbell
Born: abt. 1873, Iowa
Died: 29 July 1957, Bates, Scott, Arkansas
Source: Stutesman Family Tree-Indiana, ancestry.com
Most larger public libraries provide free access to Ancestry.com.
Born: abt. 1914
Married: 10 Oct 1939, Le Flore Co, Oklahoma
Born: abt. 1921
1940 Howe, Le Flore, OK
Jesse S. Campbell, b. AR, 25, education=8th grade, laborer farming
Bonnie L., b. OK, 19, educ=8th grade
Their neighbors were Corbie, Marie and children Campbell.
The challenge in Oklahoma is that they don't publish a death index. You have to find their cemetery or obituary record. IF this is your Jesse, he MIGHT be alive.
The Poteau Valley Genealogical Society, www.rootsweb.ancestry.com/~okleflor/pvgs.htm does do research.
You can order a copy of a death certificate from the Oklahoma State Dept Health, www.ok.gov/health/Birth_and_Death_Certificates. However, you have to provide them the death date and place. You might want to look at their web site.
Asa "Acey" Bornelious Campbell
Born: 11 June 1905, Oklahoma [actually in 1905 this was still Indian Territory]
Died: 8 Aug 1932 but doesn't say where
Source: McKinney Family Tree, ancestry.com